# Questions tagged [matrix-inverse]

For questions about inverses and pseudoinverses of matrices.

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### Confusion about the invertible condition of a banded and bordered matrix

Recently, I noticed a conclusion in the textbook "Handbook of Splines" on pages 307-308, please see screenshots as follows: Here I give an example with order $n=5$ I tried to send an e-...
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### What are known properties of matrices where off-diagonal elements are 1?

Consider a matrix where the diagonal entries are anything but the off-diagonal entries are all one. I was able to find a formula for the determinant of this matrix, but what are other known properties?...
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### How to derive the mean of inverse-Wishart distribution?

How to derive the mean of inverse-Wishart distribution in Inverse-Wishart distribution? I have no idea about it. Thanks for your help.
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### What is the expected inverse of 1 plus a Wishart distribution?

Let $$X \sim \mathcal{W}_{n} (n, \Sigma) \; \;$$ Where $\mathcal{W}$ denotes the Wishart distribution and $\Sigma \in \mathbb{R}^{q \times q}$ is the corresponding scale matrix (symmetric, positive ...
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### Direct solution to maximum likelihood computation problem using the derivative of multivariate Gaussian w.r.t. covariance matrix

For an application, I need to compute the maximum loglikelihood of data coming from a $d$-dimensional multivariate Gaussian random variable: $$\textbf{x} \sim \mathcal{N}(\boldsymbol{\mu}, \Sigma)$$ ...
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