8 problems

Let $A$ be a positive $m \times n$ matrix, let $V$ be a positive $m \times 1$ matrix, and let $W$ be a positive $1 \times n$ matrix whose entry sums agree. Let $x$ be the top-left…

Let $A$ be a positive $m \times n$ matrix, let $D(m,n)$ be the set of minor specifications described in the paper, and let $M(S)$ be the associated product of minors. For…

For $n \geq 1$, let $D(n,n)$ be the set of minor specifications described in the paper, and let $M(S)$ be the associated product of minors of a positive $n \times n$ matrix $A$. Le…

Let $A$ be a general positive $3 \times 3$ matrix, and let $\operatorname{Sink}(A)$ denote its Sinkhorn limit. An entry is said to have degree over a field if it is algebraic over…

Let $A$ be a positive $m \times n$ matrix, and let $x$ be an entry of its Sinkhorn limit, obtained by iteratively scaling so that each row sum is $1$ and each column sum is…

Lower-boundedness-constraint removal conjecture. The lower-boundedness constraint can be removed: one may turn off the projection step in Algorithm and eliminate the parameter…

Diagonal-unitary scaling conjecture. There exist diagonal unitary matrices $D_1,D_2$ such that $D_1UD_2$ is doubly quasistochastic.

Upper-bound conjecture. The number of such scalings was conjectured to be upper-bounded.