Eigenvalues and eigenvectors of supermatrices
type: Item
instance of: scholarly article
title: Eigenvalues and eigenvectors of supermatrices
zbMATH Open document ID: 0667.15007
author: Yuji Kobayashi
author: S. Nagamachi
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: Let \(\Lambda\) be a Grassmann algebra over the complex numbers, generated by a finite or infinite number of odd elements. Let \(\Lambda_ 0\) be the even part and \(\Lambda_ 1\) the odd part of \(\Lambda\). Let \(M=\left( \begin{matrix} A\quad B\\ C\quad D\end{matrix} \right)\) be an \(n\times n\) supermatrix where A and D are square with elements in \(\Lambda_ 0\) and B and C have elements in \(\Lambda_ 1\). The authors define the concepts of (super-)eigenvalue and eigenvector for M and prove that if the eigenvalues of \(\tilde A,\) the body of A, are distinct and if the eigenvalues of \(\tilde B\) are also distinct, there exists an invertible supermatrix U such that \(U^{-1}MU\) is diagonal.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 58A50
zbMATH DE Number: 4091662
zbMATH Keywords: supermatrix
zbMATH Keywords: supereigenvalue
zbMATH Keywords: supereigenvector
zbMATH Keywords: Grassmann algebra
reviewed by: Fergus J. Gaines
MaRDI profile type: Publication
full work available at URL: pjaa.64.249
OpenAlex ID: W1981203397
cites work: Q3808891
DOI: 10.3792/PJAA.64.249
description: scientific article; zbMATH DE number 4091662