# Questions tagged [matrix-inverse]

For questions about inverses and pseudoinverses of matrices.

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### Implicit function theorem / Implicit selections when Jacobian not invertible

I saw the attached result in the book by Dontchev and Rockafellar. It requires the Jacobian to be of full rank m. I suspect this condition can be further relaxed. Assume that we know that the columns ...
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### Product of matrices equal identity

I need to solve the following equation for the matrix $P \in\mathbb{R}^{r\times d}:$ $$((PAP^\top)^{-1} P S P^\top (PAP^\top)^{-1})^2 = I_r,$$ where $S$ is a symmetric $d\times d$ matrix, $A$ is a ...
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### When is $(I - X)^{-\top} \circ X = 0$?

I am currently looking at the following expression $(I - X)^{-\top} \circ X = 0$, where $\circ$ is the Hadamard product, $\top$ is the transpose, $I$ is the identity, and $X$ is non-negative and ...
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### Existence of matrices with some invertibility properties

Prove that there exists five matrices $B_i \in \mathbb{F}_2^{5\times 10}$, $i\in \{1,2,3,4,5\}$, such that any two $B_i$'s form an invertible matrix in $\mathbb{F}_2^{10\times 10}$. I am interested ... 334 views

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