On exterior powers of endomorphisms (Q1239225)

Let \(V\) be an n-dimensional vector space and \(T \in \Hom(V,V)\). The first result shows that if \(C_m(T)\), the m-th compound of \(T\), possesses a basis of eigenvectors, then lt possesses a basis consisting of decomposable eigenvectors in the m-th Grassmann space over \(V\). The paper also contains a simplified proof of a recent result of \textit{S. Be1cerzyk} [Colloq. math. 23, 203--211 (1971; Zbl 0239.13009)j on traces of compounds as well as conditions for the equality of fixed coefficients in the polynomials \( \det(\lambda A + \mu X)\) and \( \det(\lambda B + \mu X)\).