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Matrix scaling: A geometric proof of Sinkhorn's theorem

✍ Scribed by Alberto Borobia; Rafael Cantó

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
304 KB
Volume
268
Category
Article
ISSN
0024-3795

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✦ Synopsis

Matrix sealing problems have been extensively studied since Sinkhorn established in 1964 the following result: Any positive square matrix of order n is diagonally equivalent to a unique doubly stochastic matrix of order n, and the diagonal nuttriees which take part in the equivalence are unique up to scalar factors. We present a new elementary proof of the existence part of Sinldlorn's theorem which is based on well-known geometrical interpretations of doubly stochastic matrices and left and right multiplication by diagonal matrices.

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