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Let $M \in \mathbb{R}^{k\times k}$ positive definite with $\operatorname{tr} M = m$, where $m$ is an integer such that $m \geq k$. I have found a way (using this answer) to decompose $M = AA^t$ with $...

A matrix $M$ is called transposable if it can be transformed into its transpose $M^t$ via row and column permutations. Is there an efficient a way/algorithm to decide if a given matrix is ...

I am trying (and have been recommended) to use the Lanczos algorithm to find the $k$ smallest eigenvectors. However, all of the literature seems to talk about this algorithm as a way to estimate the $...

In order to pass the Cholesky decomposition, I understand the matrix must be positive definite. However, I also see that there are issues sometimes when the eigenvalues become very small but negative ...