Definition: Let f:V->V be a linear transformation on an inner product space V. The adjoint f* of f is a linear transformation f*:V->V satisfying(adsbygoogle = window.adsbygoogle || []).push({});

<f(v),w>=<v,f*(w)> for all v,w in V.

My question is would <f*(v),w>=<v,f(w)> be equivalent to the above formula in the definition? If so why?

where <,> denote inner products.

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# Adjoint of f?

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