All Questions

Let $M$ be a real square matrix of order $n\ge 3$. Assume that for every nonnegative vector $\textbf{z}\in \mathbb R^n$ which has at lease one zero entry we have $\textbf{z}^T M \textbf{z} \ge 0$. Can ...

Let $d = (d_1,...,d_k)^t$ with positive entries. Denote $D:=diag(d)$ and let $m > k$. What are sufficient conditions on $d$ and $m$ so that there exists $V \in \mathbb{R}^{m \times k}$ with: $V$ ...