3 problems

Let $A$ and $B$ be real positive definite matrices, and let a symmetric word equation be an equation obtained by evaluating a symmetric word in $A$ and $B$ at a prescribed matrix.…

Let a system of equations be a set of word equations, and call it independent if it is not equivalent to any proper subset. A system is constant-free when its equations contain onl…

The totally decomposable word conjecture. The following are equivalent: $w$ is totally decomposable; $w$ is uniquely universal; $w$ is universal; and $w(X,A)=B$ has a solution in t…