Let V be a finite-dimensional vector space over F

| August 31, 2017

Question
Let V be a finite-dimensional vector space over F, and let S, T ∈ L(V ) be linearoperators on V . Suppose that T has dim(V ) distinct eigenvalues and that, given anyeigenvector v ∈ V for T associated to some eigenvalue λ ∈ F, v is also an eigenvectorfor S associated to some (possibly distinct) eigenvalue µ ∈ F. Prove that T ◦S = S ◦T.

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