Let $P_X$ and $P_Y$ are the projection matrices into $C(X)$ and $C(Y)$, respectively.Show that $P_XP_Y = 0$ iff $C(X)\perp C(Y)$. Here $C(X),C(Y)$ mean the column spaces of the matrices $X,Y$ respectively. I don't know how to approach this. Please help!
2025-01-13 09:11:08.1736759468
Let $P_X$ and $P_Y$ are the projection matrices
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