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(This question is a repost of a deleted question I asked, because the previous version had several elements missing) Setting For fixed $N \in \mathbb{N}$, I wish to compute the entries of a matrix $...

Suppose we are given $n \times n$ rational matrix, $A$ with at most $k$ nonzero elements in each row and each column with $k \ll n$. What is the best algorithm to compute its Jordan decomposition? ...

Given two secret square matrices, say $\left( {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}}&{{a_{13}}}\\ {{a_{21}}}&{{a_{22}}}&{{a_{23}}}\\ {{a_{31}}}&{{a_{32}}}&{{a_{33}}} \...

There is an algorithm that for any input matrix $A \in \mathbb{R}^n$ satisfies $x^\top A x>0$ for all $x \in \mathbb{R}^n$, e.g. by using Cholesky algorithm. Is there an algorithm that, for matrix $...