3 problems

Prosen's conjecture. The total number of proper eigenstates of $\hat{\mathcal{M}}_{\ell,m}$ is equal to the dimension of $\mathcal{V}_{\ell,m}^r$.

Similarity characterization conjecture. The Jordan SVD exists if and only if $AB$ is similar to $BA$.

Let $M_L$ be the Markov matrix of the asymmetric annihilation model, of size $2^L$, and let an eigenvalue's multiplicity mean the number of times it occurs in the characteristic po…