Location of Ritz values in the numerical range of normal matrices

2020/04/11 by Kennett L. Dela Rosa, Rosa, Kennett L. Dela, Hugo J. Woerdeman +1
Computer Science · Mathematics · #15A18 #15A29 #15A60 #47A12 #47A20 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2004.05288

openalex publication_date 2020/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let μ₁ be a complex number in the numerical range W(A) of a normal matrix A. In the case when no eigenvalues of A lie in the interior of W(A), we identify the smallest convex region containing all possible complex numbers μ₂ for which \beginbmatrixμ₁& * 0& μ₂\endbmatrix is a 2-by-2 compression of A.

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