Principal minors and diagonal similarity of matrices
type: Item
instance of: scholarly article
title: Principal minors and diagonal similarity of matrices
zbMATH Open document ID: 0591.15005
DOI: 10.1016/0024-3795(86)90015-7
author: Raphael Loewy
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: This is a continuation of the paper of \textit{D. J. Hartfiel} and the author [ibid. 58, 147-167 (1984; Zbl 0541.15005)]. The present paper deals with the relation between diagonal similarity of two \(n\times n\) matrices A and B, with entries in a field F, and the property of A and B having equal corresponding principal minors. The main result is the following: Suppose \(n\geq 4\), A is irreducible, and for every partition of \(\{\) 1,2,...,n\(\}\) into subsets \(\alpha\), \(\beta\) with \(| \alpha | \geq 2\), \(| \beta | \geq 2\) either rank A[\(\alpha\) \(| \beta]\geq 2\) or rank A[\(\beta\) \(| \alpha]\geq 2\). If A and B have equal corresponding principal minors, of all orders, then B or \(B^ T\) is diagonally similar to A.
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 3948497
zbMATH Keywords: diagonal similarity
zbMATH Keywords: principal minors
zbMATH Keywords: irreducible
reviewed by: Mihail Voicu
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90015-7
OpenAlex ID: W2009395702
cites work: Qualitative Economics and the Scope of the Correspondence Principle
cites work: Cyclic and diagonal products on a matrix
cites work: Matrices diagonally similar to a symmetric matrix
cites work: Algorithms for Testing the Diagonal Similarity of Matrices and Related Problems
cites work: Q4767416
cites work: Q3261425
cites work: On matrices having equal corresponding principal minors
cites work: A determinantal version of the frobenius-könig theorem
cites work: Flows on graphs applied to diagonal similarity and diagonal equivalence for matrices
description: scientific article; zbMATH DE number 3948497