(a) Let and be endomorphisms of a finite dimensional vector space E such that If E has a basis of eigenvectors of and a basis of eigenvectors of then E has a basis consisting of vectors that are eigenvectors for both and (b) Interpret (a) as a statement about matrices that are similar to a diagonal...

Statement a can be interpreted as follows a If and are endomorphisms linear transformations from a v ...

(a) Let and be endomorphisms of a finite dimensional vector space E such that ...

Question:

(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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