8 problems

Let $D_1,\dots,D_d$ be positive definite $\mu\times\mu$ matrices and set … The adjugate matrix $\operatorname{Adj}[M]$ is formed from the signed minors of $M$. The adjugate hyperbo…

Coefficient-determinant positivity conjecture. The determinants of the coefficients $A_j$ of an HTM polynomial ${\bf f}_n$ are positive.

Let $P$ be a matrix polynomial, and let the upper bound in equation … is never $\infty$. Numerical experiments indicate that in many cases this upper bound is very close to the com…

Wielandt–Mirsky's conjecture. For any normal matrices $A,B\in\mathbb C^{n\times n}$ and any operator norm,

Exponent-pattern conjecture. The powers $\gamma^{K_n}$ entering $\Theta^{(N)}_{i,j}(\gamma)$ should obey the empirical rules

Let $s=s_0,dots,s_{2n-1}$ be a finite real signal decomposed into a white-noise part and an information part, and let $z\hat U_0-\hat U_1$ be the random Hankel pencil associated wi…

Perfectness conjecture. The induced quadratic module satisfies

A matrix polynomial in a single variable is a polynomial whose coefficients are matrices. A local certificate of positivity is a certificate expressing its positivity on some neigh…