Knowledge

Transformation (function)

Source 📝

34: 543: 168:" and similar), there exists an alternative form of terminological convention in which the term "transformation" is reserved only for bijections. When such a narrow notion of transformation is generalized to 547: 522: 489: 414: 387: 360: 563: 257: 568: 20: 267: 252: 133: 292: 262: 165: 145: 129: 46: 514: 352: 33: 454: 287: 149: 89: 27: 479: 404: 302: 272: 137: 121: 506: 377: 344: 430: 297: 282: 213: 38: 8: 507: 345: 277: 518: 485: 410: 383: 356: 217: 169: 100: 42: 481:
Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups
322: 557: 125: 229: 77: 69: 504: 342: 56: 141: 96: 19:"Transformation (mathematics)" redirects here. For other uses, see 212:
The set of all transformations on a given base set, together with
164:
for any function of a set into itself (especially in terms like "
65: 60: 542: 197: 509:
Classical Finite Transformation Semigroups: An Introduction
347:
Classical Finite Transformation Semigroups: An Introduction
477: 379:
Semigroups: An Introduction to the Structure Theory
513:. Springer Science & Business Media. p.  505:Olexandr Ganyushkin; Volodymyr Mazorchuk (2008). 402: 375: 351:. Springer Science & Business Media. p.  343:Olexandr Ganyushkin; Volodymyr Mazorchuk (2008). 555: 140:, and specific affine transformations, such as 484:. American Mathematical Society. p. 251. 471: 369: 155: 32: 26:For broader coverage of this topic, see 207: 556: 409:(2nd ed.). Springer. p. 29. 68:pattern. The four transformations are 16:Function that applies a set to itself 323:"Self-Map -- from Wolfram MathWorld" 160:While it is common to use the term 13: 455:"Types of Transformations in Math" 14: 580: 535: 447: 541: 258:Data transformation (statistics) 223: 21:Transformation (disambiguation) 498: 423: 396: 336: 315: 1: 478:Christopher Hollings (2014). 308: 243:+1) partial transformations. 268:Infinitesimal transformation 7: 246: 10: 585: 403:Wilkinson, Leland (2005). 376:Pierre A. Grillet (1995). 134:projective transformations 99:underpinning, that maps a 25: 18: 564:Transformation (function) 548:Transformation (function) 253:Coordinate transformation 130:geometric transformations 382:. CRC Press. p. 2. 293:Transformation semigroup 263:Geometric transformation 166:transformation semigroup 406:The Grammar of Graphics 288:Transformation geometry 156:Partial transformations 569:Functions and mappings 174:partial transformation 138:affine transformations 122:linear transformations 73: 28:Function (mathematics) 459:Basic-mathematics.com 303:Transformation matrix 273:Linear transformation 239:transformations and ( 36: 550:at Wikimedia Commons 298:Transformation group 283:Rigid transformation 228:For a finite set of 214:function composition 208:Algebraic structures 95:, usually with some 120:. Examples include 435:www.mathsisfun.com 278:List of transforms 74: 546:Media related to 524:978-1-84800-281-4 491:978-1-4704-1493-1 431:"Transformations" 416:978-0-387-24544-7 389:978-0-8247-9662-4 362:978-1-84800-281-4 218:regular semigroup 170:partial functions 576: 545: 529: 528: 512: 502: 496: 495: 475: 469: 468: 466: 465: 451: 445: 444: 442: 441: 427: 421: 420: 400: 394: 393: 373: 367: 366: 350: 340: 334: 333: 331: 329: 319: 132:, which include 119: 106:to itself, i.e. 584: 583: 579: 578: 577: 575: 574: 573: 554: 553: 538: 533: 532: 525: 503: 499: 492: 476: 472: 463: 461: 453: 452: 448: 439: 437: 429: 428: 424: 417: 401: 397: 390: 374: 370: 363: 341: 337: 327: 325: 321: 320: 316: 311: 249: 226: 210: 158: 107: 63: 50: 31: 24: 17: 12: 11: 5: 582: 572: 571: 566: 552: 551: 537: 536:External links 534: 531: 530: 523: 497: 490: 470: 446: 422: 415: 395: 388: 368: 361: 335: 313: 312: 310: 307: 306: 305: 300: 295: 290: 285: 280: 275: 270: 265: 260: 255: 248: 245: 225: 222: 209: 206: 176:is a function 162:transformation 157: 154: 82:transformation 15: 9: 6: 4: 3: 2: 581: 570: 567: 565: 562: 561: 559: 549: 544: 540: 539: 526: 520: 516: 511: 510: 501: 493: 487: 483: 482: 474: 460: 456: 450: 436: 432: 426: 418: 412: 408: 407: 399: 391: 385: 381: 380: 372: 364: 358: 354: 349: 348: 339: 324: 318: 314: 304: 301: 299: 296: 294: 291: 289: 286: 284: 281: 279: 276: 274: 271: 269: 266: 264: 261: 259: 256: 254: 251: 250: 244: 242: 238: 234: 231: 224:Combinatorics 221: 219: 215: 205: 203: 199: 195: 191: 188:, where both 187: 183: 179: 175: 171: 167: 163: 153: 151: 147: 143: 139: 135: 131: 127: 126:vector spaces 123: 118: 114: 110: 105: 102: 98: 94: 91: 87: 83: 79: 71: 67: 62: 58: 54: 48: 44: 40: 35: 29: 22: 508: 500: 480: 473: 462:. Retrieved 458: 449: 438:. Retrieved 434: 425: 405: 398: 378: 371: 346: 338: 326:. Retrieved 317: 240: 236: 235:, there are 232: 227: 211: 201: 200:of some set 193: 189: 185: 181: 177: 173: 161: 159: 150:translations 116: 112: 108: 103: 92: 85: 81: 75: 52: 230:cardinality 146:reflections 97:geometrical 78:mathematics 59:repetitive 57:rectangular 47:in SVG 39:composition 558:Categories 464:2019-12-13 440:2019-12-13 309:References 216:, forms a 53:transforms 172:, then a 142:rotations 328:March 4, 247:See also 90:function 86:self-map 43:mappings 41:of four 198:subsets 66:rhombic 64:into a 61:pattern 521:  488:  413:  386:  359:  70:linear 51:which 45:coded 88:is a 519:ISBN 486:ISBN 411:ISBN 384:ISBN 357:ISBN 330:2024 196:are 192:and 148:and 128:and 80:, a 124:of 101:set 84:or 76:In 560:: 517:. 457:. 433:. 355:. 220:. 204:. 184:→ 180:: 152:. 144:, 136:, 115:→ 111:: 55:a 37:A 527:. 515:2 494:. 467:. 443:. 419:. 392:. 365:. 353:1 332:. 241:n 237:n 233:n 202:X 194:B 190:A 186:B 182:A 178:f 117:X 113:X 109:f 104:X 93:f 72:. 49:, 30:. 23:.

Index

Transformation (disambiguation)
Function (mathematics)

composition
mappings
in SVG
rectangular
pattern
rhombic
linear
mathematics
function
geometrical
set
linear transformations
vector spaces
geometric transformations
projective transformations
affine transformations
rotations
reflections
translations
transformation semigroup
partial functions
subsets
function composition
regular semigroup
cardinality
Coordinate transformation
Data transformation (statistics)

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.