5 problems

A real matrix is normal if it commutes with its adjoint; for real matrices this means … Let a sign matrix be a matrix whose entries belong to $\{\pm1\}$. Since every real symmetric…

Let $A \in \mathbb{C}^{n\times n}$ and $\tilde{A}\in \mathbb{C}^{(n+1)\times (n+1)}$ with $n \geq 4$ be the matrices defined by … Here $\operatorname{nd}$ is the normal defect and…

Let $A \in \mathbb{C}^{n\times n}$ and $\tilde{A}\in \mathbb{C}^{(n+1)\times (n+1)}$ with $n \geq 4$ be the matrices defined by … Here $\operatorname{nd}$ denotes the normal defect…

Borcea's normal-matrix spectral-distance conjecture.

Borcea's normal-matrix invertibility conjecture. If every eigenvalue of every $B_\ell$ lies outside the unit disk and