Discriminant of the characteristic polynomial of a normal matrix
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 \(m\).
scientific article; zbMATH DE number 484257