How well can an n\(\times n\) matrix be approximated by reducible ones?
type: Item
instance of: scholarly article
title: How well can an n\(\times n\) matrix be approximated by reducible ones?
zbMATH Open document ID: 0603.47026
DOI: 10.1215/S0012-7094-86-05316-0
author: Domingo A. Herrero
author: Stanislaw J. Szarek
published in: Duke Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: There exists a universal constant \(\alpha\), \(1.7\times 10^{-7}<\alpha <\), with the following property: for each \(n\geq 2\), there exists an \(n\times n\) complex matrix \(T_ n\), with \(\| T_ n\| =1\), such that \(\| T_ n-A\| \geq \alpha\) for every reducible matrix A. The article also includes several related results.
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 47A99
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 3973659
zbMATH Keywords: reducible matrix
MaRDI profile type: Publication
cites work: On approximation of normal operators by weighted shifts
cites work: Index Theory for Perturbations of Direct Sums of Normal Operators and Weighted Shifts
cites work: Almost commuting Hermitian matrices.
cites work: Q3343152
cites work: Q5571194
cites work: Q3897665
cites work: Q3910975
cites work: Q3673508
cites work: Q5186194
cites work: A Trace Obstruction to Approximation by Block-Diagonal Nilpotents
cites work: Q3957479
cites work: Nearest normal approximation for certain operators
cites work: The finite dimensional basis problem with an appendix on nets of Grassmann manifolds
cites work: Q3040075
cites work: Q4102326
cites work: Finite Operators
full work available at URL: s0012-7094-86-05316-0
OpenAlex ID: W2088115065
description: scientific article; zbMATH DE number 3973659