Positive eigenvalues and two-letter generalized words
Christopher J. Hillar, Charles R. Johnson, Ilya M. Spitkovsky · Electronic Journal of Linear Algebra · 2002
A generalized word in two letters A and B is an expression of the formin which the exponents are nonzero real numbers.When independent positive definite matrices are substituted for A and B, it is of interest whether W necessarily has positive eigenvalues.This is known to be the case when N = 1 and has been studied in case all exponents are positive by two of the authors.When the exponent signs are mixed, however, the situation is quite different (even for 2-by-2 matrices), and this is the focus of the present work.