Question: Suppose U is a finite-dimensional real vector space and T = L(U). Prove that U has a basis consisting of eigenvectors of T if

Suppose U is a finite-dimensional real vector space and T = L(U).

Suppose U is a finite-dimensional real vector space and T = L(U). Prove that U has a basis consisting of eigenvectors of T if and only if there is an inner product on U that makes 7' into a self-adjoint operator.

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