On Exterior Powers of Endomorphisms.

摘要

Let V be an n-dimensional vector space and T a member of Hom(V,V). The first results show that if C sub m (T), the mth compound of T, possesses a basis of eigenvectors, then it possesses a basis consisting of decomposable eigenvectors in the mth Grassmann space over V. The paper also contains a simplified proof of a recent result of S. Belcerzyk on traces of compounds as well as conditions for the equality of fixed coefficients in the polynomials det(lambdaA + muX) and det(lambdaB + muX). (Author)