Normal matrices
type: Item
instance of: scholarly article
title: Normal matrices
zbMATH Open document ID: 0613.15021
DOI: 10.1016/0024-3795(87)90168-6
author: Charles R. Johnson
author: E. Marques de Sá
author: Henry Wolkowicz
author: Robert D. Grone
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: This paper gives 70 equivalent conditions for the normality of a square matrix A that involve polynomials, matrix equations, commutativity, invariant subspaces, Hermitian and skew-Hermitian parts of A and their eigenvalues, the polar factors of A and their eigenvalues, the singular values of A, trace formulas, pencil eigenvalues, the Moore-Penrose inverse, inner product equations, the field of values and more. A short discussion of proofs and references follows.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 3991706
zbMATH Keywords: normal matrix
zbMATH Keywords: normality conditions
zbMATH Keywords: polynomials
zbMATH Keywords: matrix equations
zbMATH Keywords: commutativity
zbMATH Keywords: invariant subspaces
zbMATH Keywords: Hermitian
zbMATH Keywords: skew-Hermitian
zbMATH Keywords: eigenvalues
zbMATH Keywords: polar factors
zbMATH Keywords: singular values
zbMATH Keywords: trace formulas
zbMATH Keywords: pencil eigenvalues
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: inner product equations
reviewed by: Frank Uhlig
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90168-6
OpenAlex ID: W4206092473
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description: scientific article; zbMATH DE number 3991706