On the eigenvalues of Jordan products
type: Item
instance of: scholarly article
title: On the eigenvalues of Jordan products
zbMATH Open document ID: 1020.15008
DOI: 10.1016/S0024-3795(02)00425-1
author: Enide Andrade Martins
author: F. C. Silva
published in: Linear Algebra and its Applications
publication date: 2003-03-23T00:00:00Z
review text: This paper studies the possible eigenvalues of a Jordan product \(XA + AX\) for a given \(n\) by \(n\) matrix \(A\) and varying \(X\). A matrix \(A\) is called spectrally complete, if for any given \(n\) numbers \(c_i\) there exists a nonsingular matrix \(X\) so that \(XA+AX\) has the given eigenvalues \(c_i\). If the field \(F\) is algebraically closed and has characteristic different from 2 and if \(A\) is not a multiple of the identity \(I\), then it is shown that the \(n\) by \(n\) matrix \(A\) is spectrally complete if and only if \(n \leq 2\) rank\((A)\) and the minimal polynomial of \(A\) differs from \(x^2\).
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 1886840
zbMATH Keywords: minimal polynomial
zbMATH Keywords: eigenvalue
zbMATH Keywords: Jordan product
zbMATH Keywords: spectrally complete matrix
MaRDI profile type: Publication
cites work: Eigenvalues of matrix commutators∗
cites work: On the number of invariant polynomials of matrix commutators
cites work: On the invariant polynomials of Jordan products
cites work: On the eigenvalues of the matrix
cites work: The eigenvalues of the product of matrices with prescribed similarity classes*
cites work: Existenzsätze in der Theorie der Matrizen und lineare Kontrolltheorie
full work available at URL: s0024-3795(02)00425-1
OpenAlex ID: W1987103027
description: scientific article; zbMATH DE number 1886840