Criteria for commutative factorization of a class of algebraic matrices
Analysis of PDEs
2012-11-20 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.1211.4424,
title = {Criteria for commutative factorization of a class of algebraic matrices},
author = {Andrey V. Shanin and Eugeny M. Doubravsky},
journal= {arXiv preprint arXiv:1211.4424},
year = {2012}
}