SPEKTRALE IJNTERSUCHUNG DER ABBILDUNG 5)'( 'X-N X -L XNT • - p- I - q

Abstract

SPECTRAL ANALYSIS OF MAPPING ~l:X .. N-X XNI - Description is given of the spectral analysis of mapping ~(:X .-- NqX XN,q interpreted in the space of p .q- type matrices of complex elements where Np [Gi.j-I]' 1, ] L .... p, is a nilpotent matrix of order p, and Nl is the tramposed of Nq• ?Je is shown to be a nilpotent operator with the ex- ponent p q 1: hence its eigenvectors are solutions of matrix equation NpX + XNJ ~~O For linearly independent eigenvectors Xrl; = [( _1)i Tl Gi+ j'f+ rl. i= L .... p, j = L ... , q a Jordan's chain of principal yectors is produced, demonstrating them to be of maximum length.