Schur complement formula for a diagonal entry of $(GG^\top)^{-1}$: $((GG^\top)^{-1})_{ii} = 1/\|(I-P_i)g_i\|^2$

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Schur complement formula for a diagonal entry of $(GG^\top)^{-1}$: $((GG^\top)^{-1})_{ii} = 1/\|(I-P_i)g_i\|^2$ · Prove2Me