On exterior powers of endomorphisms
Copyright policy )On exterior powers of endomorphisms
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 \( \det(\lambda B + \mu X)\).
- University of California, Santa Barbara United States
Numerical Analysis, Algebra and Number Theory, Multilinear algebra, tensor calculus, Discrete Mathematics and Combinatorics, Geometry and Topology
Numerical Analysis, Algebra and Number Theory, Multilinear algebra, tensor calculus, Discrete Mathematics and Combinatorics, Geometry and Topology
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