## Sums of Hermitian squares decomposition of non-commutative polynomials in non-symmetric variables using NCSOStools.(English)Zbl 07061310

Summary: 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.

### MSC:

 90Bxx Operations research and management science 13J30 Real algebra 90C22 Semidefinite programming 08B20 Free algebras 11E25 Sums of squares and representations by other particular quadratic forms 90C90 Applications of mathematical programming
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### References:

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