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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
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50:but its sources remain unclear because it lacks
153:Cracovians introduced the idea of using the
333:the desired effect can be achieved via the
142:requires the multiplication of the rows of
138:are column vectors and the evaluation of
81:Learn how and when to remove this message
365:Herget, Paul; (1948, reprinted 1962).
113:by hand. Such systems can be written as
16:For people from the city of Cracow, see
235:are assumed compatible for the common (
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317:Named for recognition of the City of
302:in computers of those times — mostly
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239:) type of matrix multiplication.
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177:denoted here by '∧'. Thus
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358:Banachiewicz, T. (1955).
369:(privately published).
300:sequential access memory
36:This article includes a
109:for solving systems of
65:more precise citations.
379:Kocinski, J. (2004).
202:of two matrices, say
175:matrix multiplication
402:History of astronomy
312:random access memory
304:magnetic tape memory
107:Tadeusz Banachiewicz
360:Vistas in Astronomy
345:can be obtained as
38:list of references
381:Cracovian Algebra
200:Cracovian product
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335:crossprod()
308:drum memory
288:associative
63:introducing
397:Astrometry
391:Categories
353:References
292:quasigroup
103:Cracovians
155:transpose
371:Asteroid
227:, where
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71:May 2015
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319:Cracow
242:Since
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198:. The
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