Generalized inversion of block Toeplitz matrices Original Research Article

An analog of a Wiener-Hopf factorization method is proposed for finite block Toeplitz matrices. For an arbitrary rational matrix polynomial, notions of essential indices and polynomials are introduced. A connection between these notions and a Wiener-Hopf factorization of some block triangular matrix functions is studied. A formula for a generalized (one-sided, two-sided) inversion of a block Toeplitz matrix is found in terms of indices and essential polynomials of its symbol. Well-known inversion formulas are obtained as special cases of this formula.