Let V Be A Nite Dimensional Inner Product Space And Suppose That S And T Are Sel

Completely lost in this question any help would mean so much, practice midterm question.

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

 

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