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Matrix inverse

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{wiki}

If $A$ is invertible and $1+v^TA^{-1}u\ne0$, then
$$
(A+uv^T)^{-1}
=A^{-1}-\frac{A^{-1}uv^TA^{-1}}{1+v^TA^{-1}u}.
$$

= Matrix inverses
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Sherman–Morrison formula

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 205 / 5 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 5 / e / Solution

{wiki=Sherman–Morrison_formula}

The Sherman-Morrison formula is a statement in linear algebra that provides a way to compute the inverse of a matrix when that matrix is modified by the addition of a rank-one update.


codex/matrix-inverses

Sherman–Morrison formula

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Sherman–Morrison formula

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