8 problems

Let $d$ be a positive integer, let $\mathbf{G}\in\mathbb{C}^{d\times d}$, and let $\mathbf{A}\in\mathbb{C}^{d\times d}$ be such that $\log\mathbf{A}$ exists. Suppose Definition is…

Let $n$ be a positive integer, and let … Here $p(A)$ is the polynomial evaluated at the matrix $A$, and the inequality is entrywise. Clark–Paparella conjecture. For every positive…

Ziętak's coefficient-sign conjecture. It is conjectured that $c_{k,i}<0$ for every $i\geq 1$, as long as the series for $x_k$ is not reduced to a finite series.

Complexity conjecture. The $b1$-permanent has the same computational complexity as the usual permanent for every $b1>0$.

Conjecture on improved error-estimate factors. $\gamma_1$ and $\gamma_3$ can be replaced by some other better forms, at least for $A$ real symmetric semipositive or negative, whose…

Let ${\cal B}$ be an admissible algebra, and let $GL({\cal B}^{n\times n})$ denote the invertible elements of ${\cal B}^{n\times n}$. Write $GLF({\cal B}^{n\times n})$ for the set…

Laszkiewicz et al.'s convergence conjecture. If $k\ge m-1$ and $x_0$ lies in $L^{(\operatorname{Pad\acute{e}})}_p$, then

Let $\mathcal{L}_0$ and $\mathcal{L}_1$ be matrices, and consider the quadratic matrix equation $X^2-\mathcal{L}_1X-\mathcal{L}_0=0$. A universal, possibly multivalued matrix funct…