INEQUALITIES FOR MATRIX FUNCTIONS OF COMBINATORIAL INTEREST

Author states a number of purely formal identities that are available for generalized matrix function. Some of these are generalizations of classical results for the determinant function, while others seem to be new even in the case of the determinant. A number of inequalities which compare generalized matrix functions with more familiar matrix invariants, e. g. eigenvalues are listed. Some inequalities are stated that compared values of a partlisted. Some inequalities are stated that compared values of a particular generalized matrix function on various algebraic combinations of matrices.