On Descartes' rule of signs for matrix polynomials

DOI10.7153/oam-2019-13-48zbMath1427.15010OpenAlexW2974910550MaRDI QIDQ5205407

Thomas R. Cameron, Panayiotis J. Psarrakos

Publication date: 11 December 2019

Published in: Operators and Matrices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/oam-2019-13-48

zbMATH Keywords

Hermitian matriceseigenvaluesmatrix polynomialsDescartes' rule of signsdefinite matrices

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Positive linear operators and order-bounded operators (47B65) Multilinear and polynomial operators (47H60)

Related Items (1)

Entanglement in bipartite quantum systems: Euclidean volume ratios and detectability by Bell inequalities

Cites Work

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• Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method
• Hermitian matrix polynomials with real eigenvalues of definite type. I: Classification
• Classes of linear operators. Vol. I
• Generalization and variations of Pellet's theorem for matrix polynomials
• The Quadratic Eigenvalue Problem
• Spectral Bounds for Matrix Polynomials with Unitary Coefficients
• Descartes' Rule of Signs Revisited
• Numerical Range of Matrix Polynomials
• A Simple Proof of Descartes's Rule of Signs
• Tropical Roots as Approximations to Eigenvalues of Matrix Polynomials
• Locating the Eigenvalues of Matrix Polynomials

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