3 problems

Let $\Omega_n$ be the spectral unit ball of complex $n\times n$ matrices, and let $\mathcal C_n$ denote its open subset of cyclic matrices. For $A,B\in\Omega_n$, write…

Let $A,B\in\Omega_n$, where $\Omega_n$ is the spectral ball and $A$ is cyclic, meaning that it admits a cyclic vector. The Lempert function $l_{\Omega_n}(\cdot,B)$ is considered at…

Polynomial realization conjecture. If