2 problems

Let $W$ be a word in two letters $A$ and $B$, and let $A$ and $B$ be real positive definite matrices. Trace-positivity conjecture. The word $W$ has positive trace for every pair…

Let a word be a product formed from two real positive definite matrices. A word is symmetric if it is unchanged by reversal, and a product of two symmetric words means their juxtap…