I am looking for a class of matrices $M(n(m), m, k(m), \phi)$ with the following properties: M is $n \times m$ where $n(m) > m$. Every subset of rows of size $k$ has (maximal) ra …

Given a symmetric, real $n \times n$-matrix $M$, is there a way to find all $m \times m$-submatrices ($1 < m < n$) that are nilpotent? By the Cauchy interlacing theorem, I k …

We have $2n\times 2n$ binary matrix with $k$ of its elements are $1$. We are searching for an $n\times n$ submatrix full of $1$s. What is the least $k$ such that we can always fi …

Suppose that $x \in \mathbb{R}^{n}$ is a vector of small positive fractions, i.e. $x_{i} \approx \frac{1}{n}$. The exact values are unknown. I form the matrix $M=diag(x)-\frac{xx^{ …