(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let V be a finite-dimensional inner product space, and let T be a linear operator on V. Prove that if T is invertible, then T* is invertible and (T*)^-1 = (T^-1)*

2. Relevant equations

As shown above.

<T(x),y> = <x,T*(y)>

3. The attempt at a solution

Well, I figure you only need to show that the equation holds, that shows that T* is invertible, since its inverse exists.

Now, I try to do something with the inner products:

<(T^-1)(x),y> = <x,(T^-1)*(y)>

I’m not sure how to “flip” inverse and the star.

Thanks for your help! =)

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# Homework Help: Prove adjoint invertible

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