15 problems

Matrix-analysis conjecture. Under these hypotheses,

Let $Q^{(i)}=[Q^{(i)}_{(jk)}]_{j,k=1}^2$ be arbitrary positive semidefinite $2\times2$ block matrices, and let $q^{(i)}_k$ be arbitrary non-negative numbers. For a matrix $A$, writ…

Hillar's commuting-minimizers conjecture. Such matrices $A$ and $B$ commute.

Let $A,B e 0$ be Hermitian positive semidefinite matrices of the same size, and let $Acirc B$ denote their Hadamard product. Chollet's conjecture. … The conjecture is a permanent a…

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For $A=[a_{i,j}]\in\mathcal{H}_n$, let $A(i,j)$ be obtained by deleting row $i$ and column…

Bapat–Sunder's conjecture. The largest eigenvalue of $F_A$ should satisfy

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For matrices $A=[a_{i,j}]$ and $B=[b_{i,j}]$ in $\mathcal{H}_n$, define the Hadamard product…

Positive semidefinite Graph Complement Conjecture. For any graph $G$,

Lieb–Seiringer conjecture. This coefficient is non-negative.

Novak's conjecture. The matrix

Let $A$ and $B$ be $n\times n$ positive semidefinite matrices. Let $\lambda(X)$ denote the vector of eigenvalues of a Hermitian matrix $X$, arranged in decreasing order, and let…

Let a positive semidefinite matrix in $\mathbb{M}_{2n}^{+}$ be written in blocks of the same size, with normal off-diagonal blocks. Normal-block majorization conjecture. The inequa…

Furuta's conjecture. It was asked whether

BMV conjecture, algebraic form. The polynomial $p$ has only nonnegative coefficients. This is an algebraic reformulation of the Bessis–Moussa–Villani conjecture, which originated i…

Hafnian inequality. The hafnian of this block matrix is at least