The rank of powers of matrices in a block triangular form
type: Item
instance of: scholarly article
title: The rank of powers of matrices in a block triangular form
zbMATH Open document ID: 0655.15003
DOI: 10.1016/0024-3795(88)90234-0
author: S. Friedland
author: Daniel Hershkowitz
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: A graph theoretic upper bound for the rank of sufficiently high powers of a complex valued matrix are given. Namely, assuming a lower block triangular form of the matrix, the bound is given in terms of the rank of the powers of its diagonal blocks. An index theorem, which relates the index of the matrix to the indices of its diagonal blocks, is obtained as a corollary.
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 4069077
zbMATH Keywords: graph theoretic methods
zbMATH Keywords: bounds for the rank
zbMATH Keywords: bounds for the index. index theorem
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90234-0
OpenAlex ID: W1993865925
cites work: Algebraic eigenspaces of nonnegative matrices
cites work: On Nonnegative Solutions of Matrix Equations
description: scientific article; zbMATH DE number 4069077