Unsolved Problems

Let $A,B$ be positive semidefinite, by Jensen's inequality, it is easy to see $[tr(A^s+B^s)]^{\frac{1}{s}}\leq [tr(A^r+B^r)]^{\frac{1}{r}}$, whenever ...

Problem Given a Matrix $A$, the $k$-th elementary symmetric function of $A$, namely $S_k(A)$, is defined as the sum of all $k$-by- $k$ principal mino...

Conjecture There exists a finite lattice which is not the congruence lattice of a finite algebra....

Conjecture In the category of continuous funcoids (defined similarly to the category of topological spaces) the following is a direct categorical prod...

Question I've been working on this for a long time and I'm getting nowhere. Could you help me or at least tell me where to look for help. Suppose D is...

Conjecture For $c \geq m \geq 1$, let $P(c,m)$ be the statement that given any exact $c$-coloring of the edges of a complete countably infinite graph ...

Question What is the Waring rank of the determinant of a $d \times d$ generic matrix? For simplicity say we work over the complex numbers. The $d \ti...