- #1
evilpostingmong
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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 T into a
self-adjoint operator.
The question is, what exactly do they mean by "makes T into a self adjoint
operator?" Is it that there exists an inner product of eigenvectors of T
say <v, v> that allows T to be self adjoint?
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 T into a
self-adjoint operator.
The question is, what exactly do they mean by "makes T into a self adjoint
operator?" Is it that there exists an inner product of eigenvectors of T
say <v, v> that allows T to be self adjoint?