(a) Let and be endomorphisms of a finite dimensional vector space E such that ...
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(a) Let ϕ and Ψ be endomorphisms of a finite dimensional vector space E such that ϕΨ = Ψϕ. If E has a basis of eigenvectors of ϕ and a basis of eigenvectors of Ψ then E has a basis consisting of vectors that are eigenvectors for both ϕ and Ψ.
(b) Interpret (a) as a statement about matrices that are similar to a diagonal matrix.
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Statement a can be interpreted as follows a If and are endomorphisms linear transformations from a v...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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