MINIMAL SYMMETRICAL FACTORIZATIONS OF SYMMETRICAL REAL AND COMPLEX RATIONAL MATRIX FUNCTIONS

Citation
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
Citations number
35
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
00243795
Volume
220
Year of publication
1995
Pages
249 - 282
Database
ISI
SICI code
0024-3795(1995)220:<249:MSFOSR>2.0.ZU;2-N
Abstract
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.