Bezoutians of polynomial matrices and their generalized inverses

R-Matrices and Generalized Inverses

Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of adL. For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. The constructi...

On generalized inverses of banded matrices

Bounds for the ranks of upper-right submatrices of a generalized inverse of a strictly lower k-banded matrix are obtained. It is shown that such ranks can be exactly predicted under some conditions. The proof uses the Nullity Theorem and bordering technique for generalized inverse.

Generalized Pascal Matrices and Inverses Using One-to-One Rational Polynomial s-z Transformations

Abstract: This paper proposes a one-to-one mapping between the coefficients of continuous-time (s-domain) and discrete-time (z-domain) IIR transfer functions such that the s-domain numerator/denominator coefficients can be uniquely mapped to the z-domain numerator/denominator coefficients, and vice versa. The one-to-one mapping provides a firm basis for proving the inverses of the so-called gen...

Computing Moore-Penrose Inverses of Ore Polynomial Matrices

Max-min ranks of products of two matrices and their generalized inverses

The present author recently established (J. Inequal. Appl., DOI: 10.1186/s13660016-1123-z) a group of exact formulas for calculating the maximum and minimum ranks of the products BA, and derived many algebraic properties of BA from the formulas, where A and B are two complex matrices such that the product AB is defined, and A and B are the {i, . . . , j}-inverses of A and B, respectively. As a ...