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For questions about inverses and pseudoinverses of matrices.
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Inverse of a larger matrix where the inverse of the submatrix is known
Let $A, A^{-1} \in \mathbb{R}^{n \times n}$ be known matrices. Suppose we have an invertible matrix $B \in \mathbb{R}^{(n+1) \times (n+1)}$ of the following form:
$$B = \begin{bmatrix}
A & b\\ …