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Cracovians adopted a column-row convention for designating individual elements as opposed to the standard row-column convention of matrix analysis. This made manual multiplication easier, as one needed to follow two parallel columns (instead of a vertical column and a horizontal row in the matrix
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notation.) It also sped up computer calculations, because both factors' elements were used in a similar order, which was more compatible with the
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came into general use. Any modern reference to them is in connection with their non-associative multiplication.
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will generally be different; thus, Cracovian multiplication is non-
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The computation of orbits, University of
Cincinnati Observatory
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function. Specifically, the
Cracovian product of matrices
184:. This amounts to the definition of a new type of
116:are a clerical convenience introduced in 1925 by
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61:but its sources remain unclear because it lacks
164:Cracovians introduced the idea of using the
344:the desired effect can be achieved via the
153:requires the multiplication of the rows of
149:are column vectors and the evaluation of
92:Learn how and when to remove this message
376:Herget, Paul; (1948, reprinted 1962).
124:by hand. Such systems can be written as
27:For people from the city of Cracow, see
246:are assumed compatible for the common (
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250:) type of matrix multiplication.
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301:. Cracovians are an example of a
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387:is named after the author.
188:denoted here by '∧'. Thus
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369:Banachiewicz, T. (1955).
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311:sequential access memory
47:This article includes a
120:for solving systems of
76:more precise citations.
390:Kocinski, J. (2004).
213:of two matrices, say
186:matrix multiplication
413:History of astronomy
323:random access memory
315:magnetic tape memory
118:Tadeusz Banachiewicz
371:Vistas in Astronomy
356:can be obtained as
49:list of references
392:Cracovian Algebra
211:Cracovian product
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319:drum memory
299:associative
74:introducing
408:Astrometry
402:Categories
364:References
303:quasigroup
114:Cracovians
18:Cracovians
166:transpose
382:Asteroid
238:, where
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82:May 2015
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253:Since
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209:. The
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