On exterior powers of endomorphisms
type: Item
instance of: scholarly article
title: On exterior powers of endomorphisms
zbMATH Open document ID: 0358.15030
DOI: 10.1016/0024-3795(76)90068-9
author: Marvin Marcus
author: Herbert A. Robinson
published in: Linear Algebra and its Applications
publication date: 1976-01-01T00:00:00Z
review text: Let \(V\) be an n-dimensional vector space and \(T \in \Hom(V,V)\). The first result shows that if \(C_m(T)\), the m-th compound of \(T\), possesses a basis of eigenvectors, then lt possesses a basis consisting of decomposable eigenvectors in the m-th Grassmann space over \(V\). The paper also contains a simplified proof of a recent result of \textit{S. Be1cerzyk} [Colloq. math. 23, 203--211 (1971; Zbl 0239.13009)j on traces of compounds as well as conditions for the equality of fixed coefficients in the polynomials \( \det(\lambda A + \mu X)\) and \( \det(\lambda B + \mu X)\).
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 3557971
MaRDI profile type: Publication
full work available at URL: 0024-3795(76)90068-9
OpenAlex ID: W2067775940
cites work: The Normal Form of Compound and Induced Matrices
cites work: Q5786589
cites work: On traces of exterior powers of a sum of two endomorphisms of a projective module
cites work: Q4106341
cites work: Elementary divisors of associated transformations
cites work: On direct product matrices
description: scientific article; zbMATH DE number 3557971