V is in inner product space over F and U is subspace. $p=P_u(v)$. I need to prove or disprove by an example that:
$||v||=||p||$
$<v,p>=<p,p>$
2026-04-30 02:56:49.1777517809
Inner Product and projection
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Hint: ad 1. What do you know about $\ker P_U$? Can a $v\in\ker P_U$ fulfill 1.?
ad 2. What does it mean for $P_U$ to be an orthogonal projection? Can you say something about $P_U(v-p)$?