5 problems

Johnson's inertia conjecture. If $A$ is positive definite, then

Johnson–Bapat interlacing conjecture. If $A$ is positive semidefinite and $\eta(zA,-B)$ is not identically zero, then, for every $1\leq j\leq n$, the zeros of

Johnson's conjecture. If $A$ is positive semidefinite, then the polynomial $\eta(zA,-B)$ has all real zeros.

Let $M_n(\mathbb{C})^{+}_{1}$ denote the positive semidefinite $n\times n$ complex matrices bounded above by the identity, and let $\chi_r[A]$ be the $r$-characteristic polynomial…

Let $M_n(\mathbb{C})^{+}$ denote the positive semidefinite $n\times n$ complex matrices, and let a positive contraction be a positive semidefinite matrix bounded above by the ident…