"Let T be a linear transformation on a finite dimensional real vector space V. Show that T is diagonalisable if and only if there exists an inner product on V relative to which T is self-adjoint."(adsbygoogle = window.adsbygoogle || []).push({});

The backward direction is easy. As for the forward direction, I don't understand how given an arbitrary vector space, you can go about defining an inner product without knowing something more about it.

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# Homework Help: Inner Product

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