Some Positivstellensätze for polynomial matrices
نویسندگان
چکیده
منابع مشابه
Some results on the polynomial numerical hulls of matrices
In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.
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In the context of multivariate signal processing, factorizations involving so-called para-unitary matrices are relevant as well demonstrated in the book of Vaidyanathan [11], or [4, 1] and more recently in a series of papers by McWhirter and co-authors [5, 6]. However, known factorizations of matrix polynomials, such as the Smith form [10], involve unimodular matrices but usual factorizations s...
متن کاملsome results on the polynomial numerical hulls of matrices
in this note we characterize polynomial numerical hulls of matrices $a in m_n$ such that$a^2$ is hermitian. also, we consider normal matrices $a in m_n$ whose $k^{th}$ power are semidefinite. for such matriceswe show that $v^k(a)=sigma(a)$.
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We generalize some recent results on the spectra of tridiagonal matrices, providing explicit expressions for the characteristic polynomial of some perturbed tridiagonal k-Toeplitz matrices. The calculation of the eigenvalues (and associated eigenvectors) follows straightforward. Mathematics Subject Classification: 15A18, 42C05, 33C45
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ژورنال
عنوان ژورنال: Positivity
سال: 2014
ISSN: 1385-1292,1572-9281
DOI: 10.1007/s11117-014-0312-6