The codimension of degenerate pencils
type: Item
instance of: scholarly article
title: The codimension of degenerate pencils
zbMATH Open document ID: 0487.15008
DOI: 10.1016/0024-3795(82)90003-9
author: S. Friedland
author: B. Simon
published in: Linear Algebra and its Applications
publication date: 1982-01-01T00:00:00Z
review text: The paper is devoted to the computation of the codimension of a variety of matrices. If \(d_n\) \([d_n(r)]\) denotes the codimension of the set of pairs of \(n\times n\) Hermitian [real symmetric] matrices \((A,B)\) for which \(\det(\lambda I - A - xB)= p(\lambda,x)\) is a reducible polynomial it is shown that \(d(r)\le n - 1\), \(d_n\le n - 1\) \((n\) odd), \(d_n\le n\) \((n\) even). It is shown that the equality holds for \(n=2,3\), and it is conjectured that equality holds for all \(n\).
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 3765956
zbMATH Keywords: codimension of degenerate pencils
zbMATH Keywords: variety of matrices
zbMATH Keywords: real symmetric
zbMATH Keywords: Hermitian matrices
zbMATH Keywords: reducible polynomial
MaRDI profile type: Publication
full work available at URL: 0024-3795(82)90003-9
OpenAlex ID: W2094419584
cites work: Simultaneous similarity of matrices
cites work: Analytic Properties of Bloch Waves and Wannier Functions
description: scientific article; zbMATH DE number 3765956