I already know the geometric interpretation of dot product (the length of projected vector multiply with the other vector's length)
But is there a geometric interpretation for any inner product ?
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2Check https://math.stackexchange.com/questions/476738/difference-between-dot-product-and-inner-product – Jotabeta Nov 07 '22 at 09:39
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$<u,e>e$, for e a unit vector, is the component of u in the direction e. Here u and e might be vectors in $\mathrm{R}^n$ with dot product but might also be functions with an integral inner product. – Paul Nov 07 '22 at 09:47