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Woodbury Matrix Identity

Hard · Linear Algebra & Machine Learning · Quant Trader interview question · linear-algebra, matrix-inversion, woodbury-identity

Let $A$ be an invertible $n imes n$ matrix, $U$ be an $n imes k$ matrix, $C$ be an invertible $k imes k$ matrix, and $V$ be a $k imes n$ matrix. State the Woodbury matrix identity for $(A + UCV)^{-1}$.