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In 2000, MathWorks added a
Fortran-based library for linear algebra in MATLAB 6, replacing the software's original LINPACK and EISPACK subroutines that were in C. MATLAB's Parallel Computing Toolbox was released at the 2004 Supercomputing Conference and support for graphics processing units (GPUs)
662:
By the end of the 1980s, several hundred copies of MATLAB had been sold to universities for student use. The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks. Many of the toolboxes were developed as a result of
1615:
MATLAB supports structure data types. Since all variables in MATLAB are arrays, a more adequate name is "structure array", where each element of the array has the same field names. In addition, MATLAB supports dynamic field names (field look-ups by name, field manipulations, etc.).
624:. They decided to reprogram MATLAB in C and market it for the IBM desktops that were replacing mainframe computers at the time. John Little and programmer Steve Bangert re-programmed MATLAB in C, created the MATLAB programming language, and developed features for toolboxes.
768:
programming language because types are implicitly converted. It is an inferred typed language because variables can be assigned without declaring their type, except if they are to be treated as symbolic objects, and that their type can change. Values can come from
1624:
When creating a MATLAB function, the name of the file should match the name of the first function in the file. Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores. Variables and functions are case sensitive.
616:
with 71 pre-built functions. At the time, MATLAB was distributed for free to universities. Moler would leave copies at universities he visited and the software developed a strong following in the math departments of university campuses.
2749:
In 2020, MATLAB withdrew services from two
Chinese universities as a result of US sanctions. The universities said this will be responded to by increased use of open-source alternatives and by developing domestic alternatives.
997:
Matrices can be defined by separating the elements of a row with blank space or comma and using a semicolon to separate the rows. The list of elements should be surrounded by square brackets
1941:
semantics. However, the syntax and calling conventions are significantly different from other languages. MATLAB has value classes and reference classes, depending on whether the class has
2711:
support) are implemented as wrappers around Java or ActiveX libraries. Calling MATLAB from Java is more complicated, but can be done with a MATLAB toolbox which is sold separately by
710:
The MATLAB application is built around the MATLAB programming language. Common usage of the MATLAB application involves using the "Command Window" as an interactive mathematical
702:'s functionality was expanded. By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live Editor notebook, and other features.
3026:
597:
Before version 1.0, MATLAB "was not a programming language; it was a simple interactive matrix calculator. There were no programs, no toolboxes, no graphics. And no
4113:
1452:
3146:
S.M. Rump: INTLAB – INTerval LABoratory. In Tibor
Csendes, editor, Developments in Reliable Computing, pages 77–104. Kluwer Academic Publishers, Dordrecht, 1999.
586:
and started developing MATLAB for his students as a hobby. He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor,
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4592:
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6747:
6742:
5711:
6857:
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608:
The first early version of MATLAB was completed in the late 1970s. The software was disclosed to the public for the first time in
February 1979 at the
6827:
6787:
2680:(MATLAB executables) are the dynamically loadable object files created by compiling such functions. Since 2014 increasing two-way interfacing with
6397:
651:, Inc. was founded to develop the software and the MATLAB programming language was released. The first MATLAB sale was the following year, when
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by introducing function handles, or function references, which are implemented either in .m files or anonymous/nested functions.
6288:
1975:
is an instance of a reference class, otherwise value class methods must return a new instance if it needs to modify the object.
6346:
4859:
2715:, or using an undocumented mechanism called JMI (Java-to-MATLAB Interface), (which should not be confused with the unrelated
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4852:
3931:
3813:
3344:
Chonacky, N.; Winch, D. (2005). "Reviews of Maple, Mathematica, and Matlab: Coming Soon to a
Publication Near You".
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698:
Some especially large changes to the software were made with version 8 in 2012. The user interface was reworked and
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6427:
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5126:
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in mathematics, unlike zero-based indexing commonly used in other programming languages such as C, C++, and Java.
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6501:
6383:
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565:. As of 2017, more than 5000 global colleges and universities use MATLAB to support instruction and research.
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6511:
5670:
5291:
5146:
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4702:
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2652:(GUI) applications. UIs can be generated either programmatically or using visual design environments such as
671:
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6076:
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value can actually be left out of this syntax (along with one of the colons), to use a default value of 1.
261:
3027:"An interview with CLEVE MOLER Conducted by Thomas Haigh On 8 and 9 March, 2004 Santa Barbara, California"
2982:
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https://www.mathworks.com/company/newsroom/mathworks-announces-release-2024b-of-matlab-and-simulink.html
1948:
Method call behavior is different between value and reference classes. For example, a call to a method:
6852:
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6457:
6440:
6086:
5980:
5890:
5870:
5437:
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notation is encouraged and is often faster to execute. The following code, excerpted from the function
1388:
773:, from computation involving values of other variables, or from the output of a function. For example:
218:
6571:
6526:
6326:
5975:
4188:
609:
553:
As of 2020, MATLAB has more than four million users worldwide. They come from various backgrounds of
2095:
930:) which is an array consisting of the values 1, 3, 5, 7, and 9. That is, the array starts at 1 (the
293:
6608:
6491:
6318:
6201:
5512:
5309:
5060:
4707:
4307:
3625:. Synthesis digital library of engineering and computer science. Morgan & Claypool Publishers.
2669:
2649:
1392:
1069:. For example, a submatrix taken from rows 2 through 4 and columns 3 through 4 can be written as:
1004:
are used to access elements and subarrays (they are also used to denote a function argument list).
984:
an array with the values 1, 2, 3, 4, and 5, since the default value of 1 is used as the increment.
583:
391:
4210:
667:
students that used MATLAB in academia, then brought the software with them to the private sector.
364:
128:
6807:
6722:
6364:
6293:
6071:
5941:
5396:
4875:
3865:
2716:
643:
MATLAB was first released as a commercial product in 1984 at the
Automatic Control Conference in
527:
4236:
6802:
6477:
6128:
6061:
6051:
5772:
5177:
3213:
765:
711:
682:, and for Unix PCs. Version 3 was released in 1987. The first MATLAB compiler was developed by
509:
69:
65:
61:
17:
4091:
582:. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the
6143:
6138:
6133:
6066:
6011:
4143:
3953:
3758:
3515:
3155:
Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to
Interval Analysis.
2938:
1367:
Most functions accept arrays as input and operate element-wise on each element. For example,
3586:
3552:
3168:
Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic.
3096:
6406:
6153:
6118:
6105:
5996:
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5472:
5210:
4986:
4883:
4778:
3689:
3353:
2960:
991:
613:
505:
493:
487:
460:
52:
523:
Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the
8:
6482:
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6036:
5897:
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5387:
5019:
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1431:
1249:
664:
463:
33:
4367:
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3357:
6041:
4994:
3887:
3701:
3377:
2781:
2779:
987:
683:
539:
531:
497:
423:
168:
96:
3411:
3181:
Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical
Algorithms, (2009.1).
2676:. A wrapper function is created allowing MATLAB data types to be passed and returned.
6462:
6239:
6196:
6123:
6016:
5582:
5523:
5281:
4936:
4717:
4531:
4512:
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3558:
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3493:
3369:
2801:
1938:
1396:
408:
77:
3381:
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6244:
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6001:
5880:
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5827:
5720:
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5409:
5357:
5009:
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4783:
4630:
4485:
4372:
3697:
3483:
3361:
3061:
Bezanson, Jeff; Karpinski, Stefan; Shah, Viral; Edelman, Alan (February 14, 2012).
2727:
2601:
679:
543:
455:
403:
4561:
3791:
2091:
1133:, and matrices of any size with zeros or ones can be generated with the functions
6303:
6096:
6056:
6046:
5802:
5767:
5627:
5612:
5467:
5414:
5334:
5329:
5253:
5039:
4999:
4737:
4670:
4554:
4280:
3724:
3620:
2726:
based
Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to
2105:
MATLAB has tightly integrated graph-plotting features. For example, the function
1914:
1122:
587:
547:
474:
182:
84:
6308:
6229:
5964:
5477:
5419:
5223:
2700:
2668:
MATLAB can call functions and subroutines written in the programming languages
652:
621:
517:
157:
4570:
4330:
6711:
6581:
6341:
6264:
6224:
6191:
6171:
5747:
5729:
3709:
3497:
3373:
3169:
3049:
So APL, Speakeasy, LINPACK, EISPACK, and PL0 were the predecessors to MATLAB.
2620:
2606:
1934:
1248:
or by adding dot-prime after the matrix (without the dot, prime will perform
289:
173:.m, .p, .mex*, .mat, .fig, .mlx, .mlapp, .mltbx, .mlappinstall, .mlpkginstall
5689:
6633:
6472:
6274:
6163:
6113:
6006:
5912:
5752:
5432:
5034:
4844:
2703:
can be directly called from MATLAB, and many MATLAB libraries (for example
1404:
3729:. Chapman & Hall/CRC Computer Science & Data Analysis. CRC Press.
2719:
that is also called JMI). Official MATLAB API for Java was added in 2016.
6254:
6219:
6176:
6021:
5597:
4635:
3365:
2731:
579:
554:
161:
152:
89:
6375:
4437:"US military ban locks two Chinese universities out of popular software"
3680:
Gatto, Marino; Rizzoli, Andrea (1993). "Review of MATLAB, Version 4.0".
3125:
670:
Over time, MATLAB was re-written for early operating systems created by
6541:
6283:
6026:
5922:
5812:
5787:
5777:
5636:
5592:
5271:
5200:
5138:
5085:
4655:
628:
322:
266:
199:
2090:
Graphs are unavailable due to technical issues. There is more info on
6638:
6081:
5737:
5587:
5462:
5404:
5339:
4931:
4722:
3352:(2). Institute of Electrical and Electronics Engineers (IEEE): 9–10.
2712:
2639:
2629:
2197:
1945:
as a super-class (for reference classes) or not (for value classes).
1241:
648:
644:
562:
513:
501:
327:
101:
3488:
3471:
2072:
934:
value), increments with each step from the previous value by 2 (the
6249:
5885:
5817:
5782:
5602:
5562:
5492:
5482:
5349:
5319:
5276:
5190:
5185:
5075:
4956:
4941:
4712:
4697:
2677:
699:
535:
203:
3412:"Cleve Moler: Mathematical Software Pioneer and Creator of Matlab"
2204:
6531:
6521:
5933:
5792:
5567:
5557:
5542:
5447:
5377:
5362:
5313:
5299:
5080:
5014:
4946:
4798:
4788:
4686:
4640:
2696:
2673:
938:
value), and stops once it reaches (or is about to exceed) 9 (the
591:
558:
233:
228:
223:
40:
4259:"Call Perl script using appropriate operating system executable"
6598:
6450:
6259:
5917:
5907:
5837:
5832:
5797:
5762:
5652:
5552:
5547:
5537:
5502:
5497:
5372:
5367:
5324:
5243:
5095:
5090:
5070:
4911:
4818:
4773:
4727:
4565:
3591:. SpringerLink : Bücher. Springer Netherlands. p. 1.
3339:
3337:
3335:
3333:
3331:
3329:
3327:
3325:
2738:
632:
432:
276:
271:
926:(or assigns a new value to an existing variable with the name
311:
6506:
6496:
6467:
6445:
5842:
5822:
5647:
5572:
5487:
5295:
5228:
5195:
5024:
4976:
4966:
4926:
4901:
4660:
2723:
1714:% Extract the individual red, green, and blue color channels.
578:
MATLAB was invented by mathematician and computer programmer
524:
436:
428:
416:
412:
395:
3673:
3322:
3236:"Platform Road Map for MATLAB and Simulink Product Families"
3060:
520:, and interfacing with programs written in other languages.
6588:
5757:
5532:
5425:
5303:
5286:
5233:
5218:
4971:
4692:
4650:
4620:
3578:
2688:
238:
4337:
1920:
6623:
6593:
5847:
3482:(HOPL). Association for Computing Machinery (ACM): 1–67.
2708:
2704:
675:
602:
3465:
3463:
3461:
3459:
3457:
3455:
3453:
3278:
1062:
Sets of indices can be specified by expressions such as
27:
Numerical computing environment and programming language
3509:
3507:
4388:
3588:
Numerical
Methods with Worked Examples: Matlab Edition
4468:
MATLAB: An Introduction with Applications 2nd Edition
4368:"MaMa: Calling MATLAB from Mathematica with MathLink"
3760:
System Simulation Techniques with MATLAB and Simulink
3450:
1434:
1387:
loops, but (as in other similar applications such as
760:
Variables are defined using the assignment operator,
3716:
3504:
2210:
MATLAB supports three-dimensional graphics as well:
2032:, this can be executed with the following commands:
1244:
a vector or a matrix is done either by the function
717:
612:
in California. Early versions of MATLAB were simple
4389:"MATLink: Communicate with MATLAB from Mathematica"
3750:
3612:
3546:
3544:
3517:MATLAB Programming: Mathematical Problem Solutions
1446:
869:A simple array is defined using the colon syntax:
3554:Solving Applied Mathematical Problems with MATLAB
2073:Graphics and graphical user interface programming
6709:
4528:Dynamical Systems with Applications using MATLAB
3584:
2109:can be used to produce a graph from two vectors
1978:An example of a simple class is provided below:
990:is one-based, which is the usual convention for
714:or executing text files containing MATLAB code.
4600:
4386:
3541:
3476:Proceedings of the ACM on Programming Languages
3214:"System Requirements and Platform Availability"
3093:Texas-Wisconsin Modeling and Control Consortium
4169:. Yale University, Computer Science Department
4114:"Application Programming Interfaces to MATLAB"
3157:Society for Industrial and Applied Mathematics
486:(an abbreviation of "MATrix LABoratory") is a
6391:
5949:
5719:
5705:
5154:
4860:
4586:
3343:
3284:
3261:"Matrices and Arrays - MATLAB & Simulink"
2663:
538:, adds graphical multi-domain simulation and
6753:Computer algebra system software for Windows
4874:
3679:
3646:
3622:MATLAB for Engineering and the Life Sciences
3470:Moler, Cleve; Little, Jack (June 12, 2020).
2744:
2619:3D plot of the two-dimensional unnormalized
2605:3D plot of the two-dimensional unnormalized
1687:% threshold for converting image to binary,
6728:Computer-related introductions in the 1970s
4746:
4490:Scientific Computing with MATLAB and Octave
4413:. MathWorks - File Exchange. Archived from
4365:
3840:"Create Symbolic Variables and Expressions"
3722:
3520:. De Gruyter STEM. De Gruyter. p. 21.
3469:
6748:Computer algebra system software for macOS
6743:Computer algebra system software for Linux
6664:
6398:
6384:
5956:
5942:
5712:
5698:
5161:
5147:
5121:
4867:
4853:
4593:
4579:
4233:"External Programming Language Interfaces"
3814:"Comparing MATLAB with Other OO Languages"
3618:
3304:"Current number of matlab users worldwide"
2737:Libraries also exist to import and export
1375:by 2, and then reduce each element modulo
363:
127:
6858:Proprietary commercial software for Linux
6773:Data mining and machine learning software
6405:
4366:Germundsson, Roger (September 30, 1998).
3487:
3032:. Computer History Museum. Archived from
2760:Comparison of numerical-analysis software
1855:% Now recombine to form the output image.
1418:is used here to generate square matrices
638:
635:(similar to matlab) have been available.
5168:
4509:MATLAB Codes for Finite Element Analysis
4164:
3513:
3405:
3403:
3401:
3399:
3397:
3395:
3393:
3391:
6828:Numerical analysis software for Windows
6788:Dynamically typed programming languages
4408:
3756:
3661:. Massachusetts Institute of Technology
3652:
3419:IEEE Annals of the History of Computing
2895:"Save Figure to Reopen in MATLAB Later"
1921:Classes and object-oriented programming
864:
627:Since 1993 an open source alternative,
14:
6710:
6347:Comparison of linear algebra libraries
4409:Weitzel, Michael (September 1, 2006).
4301:
3655:"Accelerating the pace of engineering"
3346:Computing in Science & Engineering
3114:
3077:
6888:Domain-specific programming languages
6868:Regression and curve fitting software
6823:Numerical analysis software for macOS
6818:Numerical analysis software for Linux
6379:
5937:
5693:
5142:
4848:
4574:
4306:. Undocumented Matlab. Archived from
3910:"Generate Field Names from Variables"
3763:. No Longer used. Wiley. p. 17.
3550:
3388:
3149:
3083:
3054:
2196:produces the following figure of the
657:Massachusetts Institute of Technology
6738:Proprietary software programmed in C
4034:"Comparing Handle and Value Classes"
3162:
3140:
2076:
1129:can be generated using the function
631:(mostly compatible with matlab) and
6863:Proprietary cross-platform software
4165:Spielman, Dan (February 10, 2004).
3585:Woodford, C.; Phillips, C. (2011).
3175:
3086:"Octave: Past, Present, and Future"
2765:List of numerical-analysis software
1908:
594:code for linear equations in 1971.
24:
6813:Mathematical optimization software
6783:Data-centric programming languages
5963:
4458:
4328:
3723:Cho, M.J.; Martinez, W.L. (2014).
3702:10.1111/j.1939-7445.1993.tb00141.x
3653:LoTurco, Lori (January 28, 2020).
534:abilities. An additional package,
25:
6899:
6878:Statistical programming languages
4546:
3409:
693:
32:For the geographical region, see
6798:High-level programming languages
6692:
6691:
6663:
6360:
6359:
6337:Basic Linear Algebra Subprograms
6095:
5120:
5109:
5108:
2638:
2628:
2203:
2081:
1780:% Make the black parts pure red.
310:
288:
6838:Numerical programming languages
6235:Seven-dimensional cross product
4429:
4402:
4380:
4359:
4322:
4302:Altman, Yair (April 14, 2010).
4295:
4273:
4251:
4225:
4203:
4181:
4158:
4132:
4106:
4084:
4062:
4040:
4026:
4004:
3990:
3968:
3946:
3924:
3902:
3880:
3858:
3832:
3806:
3784:
3425:
3296:
3285:The MathWorks (February 2020).
3253:
3228:
3206:
3184:
3084:Eaton, John W. (May 21, 2001).
3019:
2997:
1379:. MATLAB does include standard
1371:will multiply every element in
3726:Statistics in MATLAB: A Primer
3005:"Support Package Installation"
2975:
2953:
2931:
2917:"Live Code File Format (.mlx)"
2909:
2887:
2865:
2843:
2821:
1933:, virtual dispatch, packages,
980:assigns to the variable named
620:In the 1980s, Cleve Moler met
13:
1:
4012:"Object-Oriented Programming"
3514:Xue, D.; Press, T.U. (2020).
1610:
672:Digital Equipment Corporation
47:MATLAB (programming language)
6077:Eigenvalues and eigenvectors
4345:"MATLAB Engine API for Java"
3932:"Case and Space Sensitivity"
2851:"MEX Platform Compatibility"
2588:'{\bfsinc} ({\bfR})'
2393:'{\bfsinc} ({\bfR})'
1913:MATLAB supports elements of
1619:
755:
512:and data, implementation of
7:
6778:Data visualization software
6733:Array programming languages
5045:Engineering Equation Solver
4616:Advanced Simulation Library
4602:Numerical-analysis software
4235:. MathWorks. Archived from
4142:. MathWorks. Archived from
4116:. MathWorks. Archived from
4070:"Create a Simple GUIDE GUI"
4050:. MathWorks. April 30, 2011
3433:"A Brief History of MATLAB"
2983:"MATLAB App Installer File"
2753:
2648:MATLAB supports developing
2028:When put into a file named
1927:object-oriented programming
508:manipulations, plotting of
339:; 40 years ago
10:
6904:
6873:Software modeling language
4387:rsmenon; szhorvat (2013).
4376:. Wolfram Library Archive.
4304:"Java-to-Matlab Interface"
4189:"MATLAB Engine for Python"
3757:Xue, D.; Chen, Y. (2013).
2829:"Protect Your Source Code"
2664:MATLAB and other languages
2410:
2215:
573:
568:
38:
31:
6718:Image processing software
6659:
6436:
6413:
6355:
6317:
6273:
6210:
6162:
6104:
6093:
5989:
5971:
5856:
5728:
5665:
5626:
5522:
5395:
5386:
5348:
5209:
5176:
5104:
5053:
4985:
4882:
4827:
4766:
4608:
4507:Ferreira, A.J.M. (2009).
4488:; Saleri, Fausto (2006).
4470:. John Wiley & Sons.
4167:"Connecting C and Matlab"
3682:Natural Resource Modeling
3619:Tranquillo, J.V. (2011).
2745:Relations to US sanctions
922:defines a variable named
705:
690:was added to it in 2010.
610:Naval Postgraduate School
500:environment developed by
469:
454:
442:
422:
402:
387:
383:
355:
351:
333:
321:
309:
285:
257:
252:
214:
209:
197:
189:
177:
167:
151:
147:
119:
115:
107:
95:
83:
51:
6833:Numerical linear algebra
6763:Computer vision software
6758:Computer algebra systems
5513:World Programming System
4876:Computer algebra systems
4441:South China Morning Post
3557:. CRC Press. p. 6.
3421:. IEEE Computer Society.
3124:. Scilab. Archived from
2770:
2650:graphical user interface
2411:
2216:
2119:
2034:
1980:
1967:can alter any member of
1950:
1666:% for non-indexed images
1627:
1458:
1254:
1143:
1071:
1006:
951:
887:
775:
747:
728:
584:University of New Mexico
39:Not to be confused with
6768:Cross-platform software
4526:Lynch, Stephen (2004).
4211:"Call Python Libraries"
3192:"The L-Shaped Membrane"
2722:As alternatives to the
2717:Java Metadata Interface
737:'Hello, world!'
724:"Hello, world!" program
718:"Hello, world!" example
590:. This was followed by
6062:Row and column vectors
5773:FMRIB Software Library
5031:symbolic math toolbox)
4411:"MathML import/export"
3792:"MATLAB Documentation"
3063:"Why We Created Julia"
2961:"Toolbox Distribution"
1448:
639:Commercial development
316:L-shaped membrane logo
6793:Econometrics software
6407:Programming languages
6067:Row and column spaces
6012:Scalar multiplication
4120:on September 15, 2017
4092:"MATLAB App Designer"
3976:"Anonymous Functions"
3844:Symbolic Math Toolbox
3472:"A history of MATLAB"
2939:"MATLAB App Designer"
2687:Libraries written in
2615:This code produces a
2599:This code produces a
1449:
1252:for complex arrays):
1066:, which evaluates to
745:It displays like so:
370:; 15 days ago
134:; 15 days ago
6883:Time series software
6202:Gram–Schmidt process
6154:Gaussian elimination
5473:Revolution Analytics
5170:Statistical software
4779:FEATool Multiphysics
4466:Gilat, Amos (2004).
4417:on February 25, 2011
4310:on September 5, 2015
3366:10.1109/mcse.2005.39
3039:on December 27, 2014
1432:
865:Vectors and matrices
659:bought ten copies.
494:programming language
368:/ September 12, 2024
132:/ September 12, 2024
6332:Numerical stability
6212:Multilinear algebra
6187:Inner product space
6037:Linear independence
4331:"matlabcontrol JMI"
4281:"MATLAB Builder JA"
3694:1993NRM.....7...85G
3688:(1). Wiley: 85–88.
3551:Press, CRC (2008).
3358:2005CSE.....7b...9C
3128:on December 1, 2016
2873:"MAT-File Versions"
2635:
2612:
2408:
1929:including classes,
1447:{\displaystyle 1:n}
1250:conjugate transpose
530:allowing access to
464:commercial software
449:Numerical computing
306:
169:Filename extensions
108:First appeared
48:
34:Matlab (Bangladesh)
6848:Parallel computing
6843:Numerical software
6042:Linear combination
4140:"Create MEX-Files"
3998:"Nested Functions"
3954:"Function Handles"
3310:. November 9, 2017
3287:"Company Overview"
1444:
1410:for odd values of
726:exists in MATLAB.
684:Stephen C. Johnson
614:matrix calculators
540:model-based design
532:symbolic computing
375:September 12, 2024
304:
294:MATLAB Programming
139:September 12, 2024
46:
6853:Plotting software
6705:
6704:
6687:Non-English-based
6373:
6372:
6240:Geometric algebra
6197:Kronecker product
6032:Linear projection
6017:Vector projection
5931:
5930:
5687:
5686:
5661:
5660:
5136:
5135:
4842:
4841:
4762:
4761:
4537:978-0-8176-4321-8
4518:978-1-4020-9199-5
4499:978-3-540-32612-0
4486:Quarteroni, Alfio
4477:978-0-471-69420-5
4239:on March 11, 2014
3866:"Matrix Indexing"
3770:978-1-118-69437-4
3736:978-1-4665-9657-3
3632:978-1-60845-710-6
3598:978-94-007-1366-6
3564:978-1-4200-8251-7
3527:978-3-11-066370-9
3437:www.mathworks.com
3265:www.mathworks.com
3194:. MathWorks. 2003
3102:on August 9, 2017
2809:Missing or empty
2684:was being added.
2646:
2645:
2103:
2102:
1939:pass-by-reference
1642:'ecg.png'
1414:(MATLAB function
859:-1.6097 3.0000
826:12.0000 1.5708
498:numeric computing
481:
480:
305:MATLAB (software)
302:
301:
198:MATLAB Software,
153:Typing discipline
16:(Redirected from
6895:
6695:
6694:
6667:
6666:
6400:
6393:
6386:
6377:
6376:
6363:
6362:
6245:Exterior algebra
6182:Hadamard product
6099:
6087:Linear equations
5958:
5951:
5944:
5935:
5934:
5721:Image processing
5714:
5707:
5700:
5691:
5690:
5393:
5392:
5163:
5156:
5149:
5140:
5139:
5124:
5123:
5112:
5111:
4995:ClassPad Manager
4869:
4862:
4855:
4846:
4845:
4744:
4743:
4595:
4588:
4581:
4572:
4571:
4558:
4557:
4555:Official website
4541:
4522:
4503:
4481:
4453:
4452:
4450:
4448:
4433:
4427:
4426:
4424:
4422:
4406:
4400:
4399:
4397:
4395:
4384:
4378:
4377:
4373:Wolfram Research
4363:
4357:
4356:
4354:
4352:
4341:
4335:
4334:
4329:Kaplan, Joshua.
4326:
4320:
4319:
4317:
4315:
4299:
4293:
4292:
4290:
4288:
4277:
4271:
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4174:
4162:
4156:
4155:
4153:
4151:
4146:on March 3, 2014
4136:
4130:
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4110:
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4082:
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3246:
3240:de.mathworks.com
3232:
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3204:
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3182:
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3144:
3138:
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3135:
3133:
3118:
3112:
3111:
3109:
3107:
3101:
3095:. Archived from
3090:
3081:
3075:
3074:
3072:
3070:
3065:. Julia Language
3058:
3052:
3051:
3046:
3044:
3038:
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3023:
3017:
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3014:
3012:
3001:
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2836:
2825:
2819:
2818:
2812:
2807:
2805:
2797:
2795:
2793:
2783:
2642:
2632:
2592:
2589:
2586:
2583:
2580:
2577:
2576:'{\bfy}'
2574:
2571:
2568:
2565:
2564:'{\bfx}'
2562:
2559:
2556:
2553:
2550:
2547:
2544:
2541:
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2529:
2526:
2523:
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2391:
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2382:
2381:'{\bfy}'
2379:
2376:
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2370:
2369:'{\bfx}'
2367:
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2144:
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2068:
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2056:
2053:
2050:
2047:
2044:
2041:
2038:
2031:
2024:
2021:
2018:
2015:
2012:
2011:'Hello!'
2009:
2006:
2003:
1999:
1996:
1993:
1990:
1987:
1984:
1963:
1960:
1957:
1954:
1925:MATLAB supports
1909:Function handles
1904:
1901:
1898:
1895:
1892:
1889:
1886:
1883:
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1877:
1874:
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1471:
1468:
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1455:
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1382:
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1234:
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1180:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1156:
1153:
1150:
1147:
1141:, respectively.
1140:
1136:
1132:
1117:
1114:
1111:
1108:
1105:
1102:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1078:
1075:
1068:
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1058:
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1052:
1049:
1046:
1043:
1040:
1037:
1034:
1031:
1028:
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1022:
1019:
1016:
1013:
1010:
1003:
999:
983:
976:
973:
970:
967:
964:
961:
958:
955:
929:
925:
918:
915:
912:
909:
906:
903:
900:
897:
894:
891:
885:. For instance:
881:
875:
860:
857:
854:
851:
848:
845:
842:
839:
836:
833:
830:
827:
824:
821:
818:
815:
812:
809:
806:
803:
800:
797:
794:
791:
788:
785:
782:
779:
763:
751:
741:
738:
735:
732:
722:An example of a
680:Sun Microsystems
548:embedded systems
504:. MATLAB allows
477:
404:Operating system
378:
376:
371:
367:
347:
345:
340:
314:
307:
303:
292:
185:
142:
140:
135:
131:
85:Designed by
49:
45:
21:
6903:
6902:
6898:
6897:
6896:
6894:
6893:
6892:
6708:
6707:
6706:
6701:
6655:
6432:
6409:
6404:
6374:
6369:
6351:
6313:
6269:
6206:
6158:
6100:
6091:
6057:Change of basis
6047:Multilinear map
5985:
5967:
5962:
5932:
5927:
5852:
5724:
5718:
5688:
5683:
5657:
5622:
5613:The Unscrambler
5518:
5415:GraphPad InStat
5382:
5344:
5330:SOFA Statistics
5205:
5172:
5167:
5137:
5132:
5100:
5049:
5040:TI InterActive!
4981:
4878:
4873:
4843:
4838:
4823:
4758:
4742:
4604:
4599:
4553:
4552:
4549:
4544:
4538:
4525:
4519:
4506:
4500:
4484:
4478:
4465:
4461:
4459:Further reading
4456:
4446:
4444:
4443:. June 12, 2020
4435:
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4278:
4274:
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4226:
4216:
4214:
4209:
4208:
4204:
4194:
4192:
4187:
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4182:
4172:
4170:
4163:
4159:
4149:
4147:
4138:
4137:
4133:
4123:
4121:
4112:
4111:
4107:
4097:
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4089:
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4017:
4015:
4010:
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4005:
3996:
3995:
3991:
3981:
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3664:
3662:
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3601:
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3583:
3579:
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3565:
3549:
3542:
3532:
3530:
3528:
3512:
3505:
3489:10.1145/3386331
3468:
3451:
3441:
3439:
3431:
3430:
3426:
3414:
3410:Haigh, Thomas.
3408:
3389:
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2004:
2001:
1997:
1994:
1991:
1988:
1985:
1982:
1965:
1964:
1961:
1958:
1955:
1952:
1937:semantics, and
1923:
1915:lambda calculus
1911:
1906:
1905:
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1899:
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1130:
1123:identity matrix
1119:
1118:
1115:
1112:
1109:
1106:
1103:
1100:
1097:
1094:
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758:
753:
752:
749:
743:
742:
739:
736:
733:
730:
720:
708:
696:
641:
588:George Forsythe
576:
571:
528:symbolic engine
518:user interfaces
473:
379:
374:
372:
369:
343:
341:
338:
334:Initial release
317:
281:
248:
192:implementations
181:
143:
138:
136:
133:
74:object-oriented
44:
37:
28:
23:
22:
15:
12:
11:
5:
6901:
6891:
6890:
6885:
6880:
6875:
6870:
6865:
6860:
6855:
6850:
6845:
6840:
6835:
6830:
6825:
6820:
6815:
6810:
6808:Linear algebra
6805:
6800:
6795:
6790:
6785:
6780:
6775:
6770:
6765:
6760:
6755:
6750:
6745:
6740:
6735:
6730:
6725:
6723:1970s software
6720:
6703:
6702:
6700:
6699:
6689:
6684:
6679:
6674:
6660:
6657:
6656:
6654:
6653:
6646:
6641:
6636:
6631:
6626:
6621:
6616:
6611:
6606:
6601:
6596:
6591:
6586:
6585:
6584:
6574:
6569:
6564:
6559:
6554:
6549:
6544:
6539:
6534:
6529:
6524:
6519:
6514:
6509:
6504:
6499:
6494:
6489:
6488:
6487:
6486:
6485:
6480:
6465:
6460:
6455:
6454:
6453:
6443:
6437:
6434:
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6430:
6425:
6420:
6414:
6411:
6410:
6403:
6402:
6395:
6388:
6380:
6371:
6370:
6368:
6367:
6356:
6353:
6352:
6350:
6349:
6344:
6339:
6334:
6329:
6327:Floating-point
6323:
6321:
6315:
6314:
6312:
6311:
6309:Tensor product
6306:
6301:
6296:
6294:Function space
6291:
6286:
6280:
6278:
6271:
6270:
6268:
6267:
6262:
6257:
6252:
6247:
6242:
6237:
6232:
6230:Triple product
6227:
6222:
6216:
6214:
6208:
6207:
6205:
6204:
6199:
6194:
6189:
6184:
6179:
6174:
6168:
6166:
6160:
6159:
6157:
6156:
6151:
6146:
6144:Transformation
6141:
6136:
6134:Multiplication
6131:
6126:
6121:
6116:
6110:
6108:
6102:
6101:
6094:
6092:
6090:
6089:
6084:
6079:
6074:
6069:
6064:
6059:
6054:
6049:
6044:
6039:
6034:
6029:
6024:
6019:
6014:
6009:
6004:
5999:
5993:
5991:
5990:Basic concepts
5987:
5986:
5984:
5983:
5978:
5972:
5969:
5968:
5965:Linear algebra
5961:
5960:
5953:
5946:
5938:
5929:
5928:
5926:
5925:
5920:
5915:
5910:
5905:
5900:
5894:
5893:
5888:
5883:
5878:
5873:
5868:
5862:
5860:
5854:
5853:
5851:
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5815:
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5805:
5800:
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5760:
5755:
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5717:
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5709:
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5694:
5685:
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5674:
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5663:
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5615:
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5605:
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5475:
5470:
5465:
5460:
5455:
5450:
5445:
5440:
5435:
5429:
5422:
5420:GraphPad Prism
5417:
5412:
5407:
5401:
5399:
5397:Cross-platform
5390:
5384:
5383:
5381:
5380:
5375:
5370:
5365:
5360:
5354:
5352:
5346:
5345:
5343:
5342:
5337:
5332:
5327:
5322:
5317:
5307:
5294:(statsmodels,
5289:
5284:
5279:
5274:
5269:
5251:
5246:
5241:
5236:
5231:
5226:
5221:
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5022:
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5002:
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4991:
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4954:
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4606:
4605:
4598:
4597:
4590:
4583:
4575:
4569:
4568:
4559:
4548:
4547:External links
4545:
4543:
4542:
4536:
4530:. Birkhäuser.
4523:
4517:
4504:
4498:
4482:
4476:
4462:
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3449:
3424:
3387:
3321:
3295:
3277:
3252:
3227:
3205:
3183:
3174:
3172:, 19, 287–449.
3161:
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1981:
1951:
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1907:
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1621:
1618:
1612:
1609:
1459:
1443:
1440:
1437:
1255:
1144:
1072:
1007:
1000:. Parentheses
952:
888:
866:
863:
776:
764:. MATLAB is a
757:
754:
748:
729:
719:
716:
707:
704:
695:
694:Recent history
692:
686:in the 1990s.
653:Nick Trefethen
640:
637:
622:John N. Little
575:
572:
570:
567:
516:, creation of
491:multi-paradigm
479:
478:
471:
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458:
452:
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440:
439:
426:
420:
419:
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380:
361:
359:
357:Stable release
353:
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121:Stable release
117:
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93:
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81:
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58:multi-paradigm
55:
26:
9:
6:
4:
3:
2:
6900:
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6829:
6826:
6824:
6821:
6819:
6816:
6814:
6811:
6809:
6806:
6804:
6803:IRIX software
6801:
6799:
6796:
6794:
6791:
6789:
6786:
6784:
6781:
6779:
6776:
6774:
6771:
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6607:
6605:
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6597:
6595:
6592:
6590:
6587:
6583:
6582:Object Pascal
6580:
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6469:
6466:
6464:
6461:
6459:
6456:
6452:
6449:
6448:
6447:
6444:
6442:
6439:
6438:
6435:
6429:
6426:
6424:
6421:
6419:
6416:
6415:
6412:
6408:
6401:
6396:
6394:
6389:
6387:
6382:
6381:
6378:
6366:
6358:
6357:
6354:
6348:
6345:
6343:
6342:Sparse matrix
6340:
6338:
6335:
6333:
6330:
6328:
6325:
6324:
6322:
6320:
6316:
6310:
6307:
6305:
6302:
6300:
6297:
6295:
6292:
6290:
6287:
6285:
6282:
6281:
6279:
6277:constructions
6276:
6272:
6266:
6265:Outermorphism
6263:
6261:
6258:
6256:
6253:
6251:
6248:
6246:
6243:
6241:
6238:
6236:
6233:
6231:
6228:
6226:
6225:Cross product
6223:
6221:
6218:
6217:
6215:
6213:
6209:
6203:
6200:
6198:
6195:
6193:
6192:Outer product
6190:
6188:
6185:
6183:
6180:
6178:
6175:
6173:
6172:Orthogonality
6170:
6169:
6167:
6165:
6161:
6155:
6152:
6150:
6149:Cramer's rule
6147:
6145:
6142:
6140:
6137:
6135:
6132:
6130:
6127:
6125:
6122:
6120:
6119:Decomposition
6117:
6115:
6112:
6111:
6109:
6107:
6103:
6098:
6088:
6085:
6083:
6080:
6078:
6075:
6073:
6070:
6068:
6065:
6063:
6060:
6058:
6055:
6053:
6050:
6048:
6045:
6043:
6040:
6038:
6035:
6033:
6030:
6028:
6025:
6023:
6020:
6018:
6015:
6013:
6010:
6008:
6005:
6003:
6000:
5998:
5995:
5994:
5992:
5988:
5982:
5979:
5977:
5974:
5973:
5970:
5966:
5959:
5954:
5952:
5947:
5945:
5940:
5939:
5936:
5924:
5921:
5919:
5916:
5914:
5911:
5909:
5906:
5904:
5901:
5899:
5896:
5895:
5892:
5889:
5887:
5884:
5882:
5879:
5877:
5874:
5872:
5869:
5867:
5864:
5863:
5861:
5859:
5855:
5849:
5846:
5844:
5841:
5839:
5836:
5834:
5831:
5829:
5826:
5824:
5821:
5819:
5816:
5814:
5811:
5809:
5806:
5804:
5801:
5799:
5796:
5794:
5791:
5789:
5786:
5784:
5781:
5779:
5776:
5774:
5771:
5769:
5766:
5764:
5761:
5759:
5756:
5754:
5751:
5749:
5748:CellCognition
5746:
5744:
5741:
5739:
5736:
5735:
5733:
5731:
5727:
5722:
5715:
5710:
5708:
5703:
5701:
5696:
5695:
5692:
5680:
5679:
5675:
5673:
5672:
5668:
5667:
5664:
5654:
5651:
5649:
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5643:
5640:
5638:
5635:
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5632:
5629:
5625:
5619:
5616:
5614:
5611:
5609:
5606:
5604:
5601:
5599:
5596:
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5591:
5589:
5586:
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5514:
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5509:
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5501:
5499:
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5491:
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5411:
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5400:
5398:
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5391:
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5379:
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5364:
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5353:
5351:
5347:
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5338:
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5331:
5328:
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5323:
5321:
5318:
5315:
5311:
5308:
5305:
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5293:
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5280:
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5275:
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5250:
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5232:
5230:
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5217:
5216:
5214:
5212:
5208:
5202:
5199:
5197:
5194:
5192:
5189:
5187:
5184:
5183:
5181:
5179:
5178:Public domain
5175:
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5164:
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5145:
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5141:
5129:
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5119:
5117:
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5097:
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4898:
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4442:
4438:
4432:
4416:
4412:
4405:
4390:
4383:
4375:
4374:
4369:
4362:
4351:September 15,
4346:
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4309:
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4276:
4260:
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4238:
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4228:
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4119:
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4093:
4087:
4071:
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4029:
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3993:
3977:
3971:
3955:
3949:
3933:
3927:
3911:
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3883:
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3861:
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3835:
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3809:
3793:
3787:
3772:
3766:
3762:
3761:
3753:
3742:September 17,
3738:
3732:
3728:
3727:
3719:
3711:
3707:
3703:
3699:
3695:
3691:
3687:
3683:
3676:
3665:September 16,
3660:
3656:
3649:
3638:September 17,
3634:
3628:
3624:
3623:
3615:
3604:September 16,
3600:
3594:
3590:
3589:
3581:
3570:September 16,
3566:
3560:
3556:
3555:
3547:
3545:
3533:September 16,
3529:
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3519:
3518:
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3499:
3495:
3490:
3485:
3481:
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3178:
3171:
3170:Acta Numerica
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2803:
2792:September 15,
2788:
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2775:
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2641:
2637:
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2631:
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2626:
2622:
2621:sinc function
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2608:
2607:sinc function
2604:
2603:
2598:
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2407:
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2211:
2208:
2206:
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2199:
2198:sine function
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2097:
2096:MediaWiki.org
2093:
2088:
2079:
2078:
2033:
1979:
1976:
1974:
1970:
1949:
1946:
1944:
1940:
1936:
1935:pass-by-value
1932:
1928:
1918:
1916:
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1617:
1457:
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1409:
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1394:
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993:
989:
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950:
948:
943:
941:
937:
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886:
884:
878:
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805:'hat'
774:
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767:
750:Hello, world!
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701:
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475:mathworks.com
472:
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210:Influenced by
208:
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201:
196:
193:
188:
184:
183:mathworks.com
180:
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75:
71:
67:
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6682:Generational
6672:Alphabetical
6668:
6648:
6566:
6473:Visual Basic
6275:Vector space
6007:Vector space
5913:MountainsMap
5902:
5753:CellProfiler
5676:
5669:
5457:
5433:SPSS Modeler
5265:
5261:
5257:
5125:
5113:
5054:Discontinued
5035:SMath Studio
5028:
4831:
4808:
4747:Discontinued
4682:
4678:
4674:
4527:
4511:. Springer.
4508:
4492:. Springer.
4489:
4467:
4445:. Retrieved
4440:
4431:
4419:. Retrieved
4415:the original
4404:
4392:. Retrieved
4382:
4371:
4361:
4349:. Retrieved
4339:
4324:
4312:. Retrieved
4308:the original
4297:
4285:. Retrieved
4275:
4263:. Retrieved
4253:
4241:. Retrieved
4237:the original
4227:
4215:. Retrieved
4205:
4193:. Retrieved
4183:
4171:. Retrieved
4160:
4148:. Retrieved
4144:the original
4134:
4122:. Retrieved
4118:the original
4108:
4096:. Retrieved
4086:
4074:. Retrieved
4064:
4052:. Retrieved
4048:"MATLAB GUI"
4042:
4036:. MathWorks.
4028:
4016:. Retrieved
4006:
4000:. MathWorks.
3992:
3980:. Retrieved
3970:
3958:. Retrieved
3948:
3936:. Retrieved
3926:
3914:. Retrieved
3904:
3892:. Retrieved
3888:"Structures"
3882:
3870:. Retrieved
3860:
3848:. Retrieved
3843:
3834:
3822:. Retrieved
3817:
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3796:. Retrieved
3786:
3774:. Retrieved
3759:
3752:
3740:. Retrieved
3725:
3718:
3685:
3681:
3675:
3663:. Retrieved
3658:
3648:
3636:. Retrieved
3621:
3614:
3602:. Retrieved
3587:
3580:
3568:. Retrieved
3553:
3531:. Retrieved
3516:
3479:
3475:
3442:September 4,
3440:. Retrieved
3436:
3427:
3418:
3349:
3345:
3312:. Retrieved
3307:
3298:
3280:
3268:. Retrieved
3264:
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3245:December 22,
3243:. Retrieved
3239:
3230:
3218:. Retrieved
3208:
3196:. Retrieved
3186:
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3142:
3130:. Retrieved
3126:the original
3116:
3104:. Retrieved
3097:the original
3092:
3079:
3067:. Retrieved
3056:
3048:
3041:. Retrieved
3034:the original
3021:
3009:. Retrieved
2999:
2987:. Retrieved
2977:
2965:. Retrieved
2955:
2943:. Retrieved
2933:
2921:. Retrieved
2911:
2899:. Retrieved
2889:
2877:. Retrieved
2867:
2855:. Retrieved
2845:
2833:. Retrieved
2823:
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2790:. Retrieved
2748:
2736:
2721:
2686:
2667:
2658:App Designer
2657:
2653:
2647:
2616:
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2209:
2202:
2195:
2117:. The code:
2114:
2110:
2106:
2104:
2027:
1977:
1972:
1968:
1966:
1947:
1942:
1924:
1912:
1882:greenChannel
1807:greenChannel
1738:greenChannel
1623:
1614:
1411:
1407:
1405:magic square
1403:, creates a
1400:
1376:
1372:
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882:
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868:
766:weakly typed
759:
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661:
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626:
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362:R2024b
323:Developer(s)
296:at Wikibooks
126:R2024b
29:
6677:Categorical
6255:Multivector
6220:Determinant
6177:Dot product
6022:Linear span
5898:Mathematica
5858:Proprietary
5598:StatsDirect
5453:Mathematica
5211:Open-source
5020:Mathematica
4987:Proprietary
4884:Open-source
4804:Mathematica
4767:Proprietary
4447:November 6,
4347:. MathWorks
4283:. MathWorks
4265:November 7,
4261:. MathWorks
4213:. MathWorks
4191:. MathWorks
4098:November 1,
4094:. MathWorks
4072:. MathWorks
4014:. MathWorks
3978:. MathWorks
3956:. MathWorks
3938:November 1,
3934:. MathWorks
3912:. MathWorks
3890:. MathWorks
3868:. MathWorks
3846:. MathWorks
3820:. MathWorks
3794:. MathWorks
3776:October 15,
3216:. MathWorks
3198:February 7,
3132:December 1,
3106:December 1,
3069:December 1,
3043:December 6,
3011:November 1,
3007:. MathWorks
2989:November 1,
2985:. MathWorks
2967:November 1,
2963:. MathWorks
2945:November 1,
2941:. MathWorks
2923:November 1,
2919:. MathWorks
2901:November 1,
2897:. MathWorks
2879:November 1,
2875:. MathWorks
2857:November 1,
2853:. MathWorks
2835:November 1,
2831:. MathWorks
2732:Mathematica
2092:Phabricator
1931:inheritance
1900:rgbImageOut
1888:blueChannel
1858:rgbImageOut
1840:binaryImage
1831:blueChannel
1816:binaryImage
1792:binaryImage
1759:blueChannel
1690:binaryImage
1426:containing
1242:Transposing
1021:16 3 2 13
580:Cleve Moler
555:engineering
488:proprietary
461:Proprietary
90:Cleve Moler
6712:Categories
6542:JavaScript
6418:Comparison
6289:Direct sum
6124:Invertible
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