A note on a determinantal inequality
type: Item
instance of: scholarly article
title: A note on a determinantal inequality
zbMATH Open document ID: 0708.15008
DOI: 10.1016/0024-3795(90)90318-7
author: S. Friedland
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: Let \(\| \cdot \|\) denote an operator norm on the set \(M_ n({\mathbb{C}})\) of \(n\times n\) matrices over the complex numbers, and let \(A,B\in M_ n({\mathbb{C}})\). Then the following inequality holds: \[ | \det (B)-\det (A)| \leq \frac{\| B\|^ n-\| A\|^ n}{\| B\| -\| A\|}\| B-A\|. \] Equality will be attained for scalar matrices A and B of the same sign. This improves an earlier result by the same author [Linear Multilinear Algebra 12, 81-98 (1982; Zbl 0491.15002)].
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 4163082
zbMATH Keywords: determinantal inequality
zbMATH Keywords: Fréchet derivative
zbMATH Keywords: norms of matrices
MaRDI profile type: Publication
full work available at URL: 0024-3795(90)90318-7
OpenAlex ID: W1969243747
cites work: Q3996765
cites work: Variation of tensor powers and spectrat
cites work: Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix
description: scientific article; zbMATH DE number 4163082