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arXiv · 2207.00840

Extensions of S-Lemma for Noncommutative Polynomials

Feng Guo·Sizhuo Yan·Lihong Zhi
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Abstract

We consider the problem of extending the classical S-lemma from commutative case to noncommutative cases. We show that a symmetric quadratic homogeneous matrix-valued polynomial is positive semidefinite if and only if its coefficient matrix is positive semidefinite. Then we extend the S-lemma to three kinds of noncommutative polynomials: noncommutative polynomials whose coefficients are real numbers, matrix-valued noncommutative polynomials and hereditary polynomials.

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Feng Guo, Sizhuo Yan, Lihong Zhi. 2022-07-02. Extensions of S-Lemma for Noncommutative Polynomials. https://arxiv.org/abs/2207.00840

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