Conceição, Ana C.Kravchenko, ViktorTeixeira, Francisco S.Bottcher, A.Kaashoek, M. A.Lebre, A. B.DosSantos, A. F.Speck, F. O.2020-08-062020-08-06200397830348940129783034880077publons.com/p/11645406/http://hdl.handle.net/10400.1/14627The explicit factorization of matrix functions of the form Agamma(b) = ( (e)(b*) (b)(b*b)(+ gammae)), where b is an n x n matrix function, a represents the identity matrix, and gamma is a complex constant, is studied. To this purpose some relations between a factorization of A, and the resolvents of the self-adjoint operators N+ (b) = P(+)bP(-)b*P+ and N- (b) = P(-)b*P(+)bP(-) are analyzed. The main idea is to show that if b is a matrix function that can be represented through the decomposition b = b(-) + b(+) where at least one of the summands is a rational matrix, then it is possible to construct an algorithm that allows us to determine an effective canonical factorization of the matrix function A(gamma).engbook part2020-08-06cv-prod-198089410.1007/978-3-0348-8007-7_5