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## Main Question or Discussion Point

Definition from my textbook: For each linear operator T on a inner product space V, the

My instructor defined it by <T(v),w> = <v,T*(w)> and he said that these 2 definitions are

Now, can someone please explain WHY they are equaivalent?

Can both definitions be used at the SAME time, or do I have to choose 1 of the 2 definitions and use this chosen definition

Thanks for explaining!

**adjoint**of T is the mapping T* of V into V that is defined by the equation <T*(v),w> = <v,T(w)> for all v, w E V.My instructor defined it by <T(v),w> = <v,T*(w)> and he said that these 2 definitions are

*equivalent*.Now, can someone please explain WHY they are equaivalent?

Can both definitions be used at the SAME time, or do I have to choose 1 of the 2 definitions and use this chosen definition

*consistently*everywhere?Thanks for explaining!