The positive trace conjecture for words in two positive definite matrices

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 juxtaposition. Positive trace conjecture. A word has positive trace for every pair of real positive definite matrices if and only if the word is symmetric or a product of two symmetric words. This conjecture concerns the characterization of words whose trace is always positive; the supplied text gives no resolution status.