Eigenvalue location of certain matrix polynomials

2023/02/14 by B, Pallavi, Hadimani, Shrinath, Jayaraman, Sachindranath
#15A18 #15A22 #15B51 #47A56 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2302.06788

Abstract

It is known that a matrix polynomial with unitary matrix coefficients has its eigenvalues in the annular region (1)/(2) < |λ| < 2. We prove in this short note that under certain assumptions, matrix polynomials with either doubly stochastic matrix coefficients or Schur stable matrix coefficients also have eigenvalues in similar annular regions.

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