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Let V be a nite-dimensional inner product space and suppose that S and T are self-adjoint. Prove that if ST 2 TS then there exists an orthonormal...

Screen Shot 2018-08-07 at 9.48.32 PM.pngCompletely lost in this question any help would mean so much, practice midterm question.

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Let V be a finite-dimensional inner product space and suppose that S
and T are self-adjoint. Prove that if ST 2 TS then there exists an
orthonormal basis ('01, . . . gun) of V which is an eigenbasis for both 8
and T. (hint: the A-eigenspace for 8' is invariant for T and Vice versa)

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