Theorem demonstrates a positive definite structure in noncommutative settings, suggesting applications in linear algebra.
Hunter proved that the complete homogeneous symmetric polynomials of even degree are positive definite. We prove a noncommutative generalization of this result, in which the scalar variables are replaced with hermitian operators. We provide a sharp lower bound and a sum of hermitian squares representation that are novel even in the scalar case.
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Garcia et al. (2025) studied this question.
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