Self-interlacing polynomials II: Matrices with self-interlacing spectrum

2016/12/05 by Mikhail Tyaglov, Tyaglov, Mikhail
Computer Science · Materials Science · Mathematics · #12D10 #15A18 #15B05 #15B35 #15B48 #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Liquid Crystal Research Advancements #Matrix Theory and Algorithms #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1612.05102

openalex publication_date 2016/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An n× n matrix is said to have a self-interlacing spectrum if its eigenvalues λ_k, k=1,…,n, are distributed as follows λ₁gt;-λ₂gt;λ₃gt;\cdotsgt;(-1)^n-1λ_ngt;0. A method for constructing sign definite matrices with self-interlacing spectra from totally nonnegative ones is presented. We apply this method to bidiagonal and tridiagonal matrices. In particular, we generalize a result by O. Holtz on the spectrum of real symmetric anti-bidiagonal matrices with positive nonzero entries.

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