The number of nonconstant invariant polynomials of matrices with several prescribed blocks
type: Item
instance of: scholarly article
title: The number of nonconstant invariant polynomials of matrices with several prescribed blocks
zbMATH Open document ID: 1031.15013
DOI: 10.1016/S0024-3795(02)00660-2
author: Glória Cravo
author: F. C. Silva
published in: Linear Algebra and its Applications
publication date: 2003-07-30T00:00:00Z
review text: Let \(C=M_n(F)\) be a square matrix partitioned into \(k\times k\) blocks \([C_{i,j}]\) such that the diagonal blocks \(C_{1,1},\dots,C_{k,k}\) are square. The main theorem of this paper claims that: Let \(F\) be an algebraically closed field, \(\sigma\in S_k\) be a permutation, and \(A_{j,\sigma(j)}\) (\(1\leq j\leq k\)) be given matrices. Then the interval of the number \(i(C)\) of nonconstant invariant polynomials is given where the blocks \(C_{j,\sigma(j)}=A_{j,\sigma(j)}\) of \(C\) are fixed for every \(1\leq j\leq k\).
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 1956795
zbMATH Keywords: invariant polynomial
zbMATH Keywords: block matrix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1956795