Cayley-Hamilton theorem for mixed discriminants

Article Type

Research Article

Publication Title

Journal of Combinatorial Mathematics and Combinatorial Computing

Abstract

The mixed discriminant of an n-Tuple of nxn matrices A1,..., An is defined as D(A1,A2.....An)=1/n! Σσ∈S(n) det(A(2)σ1A(1)σ2,...,Anσn), where denotes the z'th column of the matrix A and S(n) denotes the group of permutations of 1,2,... ,n. For n matrices A\>...y An and indeterminates λ1 λn,set φ λ1 λn A1,..., An, set = D(λ1 I-A1,..λn I-An). It is shown that φ A1,..., An = 0.

First Page

223

Last Page

231

Publication Date

5-1-2017

This document is currently not available here.

Share

COinS