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arXiv · 1211.4424

Criteria for commutative factorization of a class of algebraic matrices

Andrey V. Shanin·Eugeny M. Doubravsky
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Abstract

The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation formulae are derived. Necessary condition for commutative factorization is found for a class of "balanced" matrices. Together with Moiseyev's method and Hurd's idea, this gives a description of the class of commutatively solvable matrices. As a result, a simple analytical procedure is described, providing an answer, whether a given matrix is commutatively factorizable or not.

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Andrey V. Shanin, Eugeny M. Doubravsky. 2012-11-19. Criteria for commutative factorization of a class of algebraic matrices. https://arxiv.org/abs/1211.4424

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