MINIMAL SYMMETRICAL FACTORIZATIONS OF SYMMETRICAL REAL AND COMPLEX RATIONAL MATRIX FUNCTIONS

Real and complex rational matrix functions W(lambda) such that W(lambd a) = xi[W(eta lambda)](T), where xi, eta = +/-1, and their minimal fac torizations W(lambda) = [L(eta lambda)]D-T(lambda)L(lambda) are studie d. Such factorizations are described geometrically in terms of invaria nt subspaces with certain isotropic properties with respect to a quadr atic form. Using results (partly known and partly proved in the paper) concerning the dimensions of such subspaces, upper bounds are given f or the degrees of the rational matrix functions L(lambda) in the above factorizations.