Abstract

Numerous applied problems contain matrices as variables, and the formulas therefore involve polynomials in matrices. To handle such polynomials it is necessary study non-commutative polynomials. In this paper we will present an algorithm and its implementation in the free Matlab package NCSOStools using semidefinite programming to check whether a given non-commutative polynomial in non-symmetric variables can be written as a sum of Hermitian squares.

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