P. Lancaster et L. Rodman, MINIMAL SYMMETRICAL FACTORIZATIONS OF SYMMETRICAL REAL AND COMPLEX RATIONAL MATRIX FUNCTIONS, Linear algebra and its applications, 220, 1995, pp. 249-282
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.