Discriminant of the characteristic polynomial of a normal matrix
type: Item
instance of: scholarly article
title: Discriminant of the characteristic polynomial of a normal matrix
zbMATH Open document ID: 0796.15009
DOI: 10.1007/BF01206384
author: N. V. Ilyushechkin
published in: Mathematical Notes
publication date: 1994-02-08T00:00:00Z
review text: The article contains a generalization of a previous result of the author concerning the expression of the discriminant of the characteristic polynomial of a symmetric matrix in terms of its elements. It is shown that if \(D(Z)\) is the discriminant of the characteristic polynomial of a normal matrix \(Z \in \mathbb{C}^{n \times n}\) then \(| D(Z) |\) is the sum of squares of all minors of maximal order of a matrix \(Z_ *\); here \(Z_ *\) is a matrix of size \(n^ 2 \times n\) whose \(m\)-th column, \(m=0,1,\dots,n-1\), contains the elements of the matrix \(Z^ m\) taken in the same order for all \(m\).
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 484257
zbMATH Keywords: discriminant
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: symmetric matrix
zbMATH Keywords: normal matrix
MaRDI profile type: Publication
cites work: Q3688508
cites work: Q5818478
description: scientific article; zbMATH DE number 484257