On the Segre characteristic of a block triangular matrix
type: Item
instance of: scholarly article
title: On the Segre characteristic of a block triangular matrix
zbMATH Open document ID: 0945.15007
DOI: 10.1016/S0024-3795(99)00094-4
author: Rafael Cantó
author: Ana M. Urbano
published in: Linear Algebra and its Applications
publication date: 2000-10-08T00:00:00Z
review text: Consider two complex matrices \(A\) and \(B\) of sizes \(n\times n\) and \(m\times m\) respectively, and let \(\lambda\) be an eigenvalue of both matrices. If \(\alpha= (n_1,n_2)\) and \(\beta= (m_1,m_2)\) are the Segre characteristics associated with \(\lambda\) of \(A\) and \(B\), respectively, and \(\gamma= (r_1,r_2, r_3,r_4)\) is a nonincreasing sequence of nonnegative integers, then a method for determining when \(\gamma\) is the Segre characteristic of the block triangular matrix \[ M=\left[ \begin{matrix} A & L \\ 0 & B\end{matrix} \right] \] in terms of \(\alpha\) and \(\beta\), and the structure of the matrix \(L\) is presented. A complete explicit description of the Segre characteristic of \(M\) associated with \(\lambda\) is obtained. Using similar techniques, general cases when \(\alpha,\beta\) and \(\gamma\) have more elements and satisfy some size restrictions are considered.
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 1419869
zbMATH Keywords: Segre characteristics
zbMATH Keywords: block triangular matrix
zbMATH Keywords: Carlson problem
zbMATH Keywords: Jordan canonical form
reviewed by: Rodica Covaci
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1419869