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• W2012806883 abstract "Let M be an archimedean quadratic module of real t-by-t matrix polynomials in n variables, and let S be the set of all real n-tuples where each element of M is positive semidefinite. Our key finding is a natural bijection between the set of pure states of M and the cartesian product of S with the real projective (t-1)-space. This leads us to conceptual proofs of positivity certificates for matrix polynomials, including the recent seminal result of Hol and Scherer: If a symmetric matrix polynomial is positive definite on S, then it belongs to M. We also discuss what happens for non-symmetric matrix polynomials or in the absence of the archimedean assumption, and review some of the related classical results. The methods employed are both algebraic and functional analytic." @default.
• W2012806883 created "2016-06-24" @default.
• W2012806883 creator A5065891534 @default.
• W2012806883 creator A5085418158 @default.
• W2012806883 date "2010-01-01" @default.
• W2012806883 modified "2023-09-27" @default.
• W2012806883 title "Pure states, positive matrix polynomials and sums of hermitian squares" @default.
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• W2012806883 doi "https://doi.org/10.1512/iumj.2010.59.4107" @default.
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