Abstract
A solution to the problem of a closed-form representation for the inverse of a matrix polynomial about a unit root is provided by resorting to a Laurent expansion in matrix notation, whose principal-part coefficients turn out to depend on the non-null derivatives of the adjoint and determinant of the matrix polynomial at the root.
Some basic relationships between principal-part structure and rank properties of algebraic function of the matrix polynomial at the unit root as well as informative closed-form expressions for the leading coefficient matrices of the matrix-polynomial inverse are established.
Lingua originale | English |
---|---|
pagine (da-a) | 541-556 |
Numero di pagine | 16 |
Rivista | LINEAR & MULTILINEAR ALGEBRA |
DOI | |
Stato di pubblicazione | Pubblicato - 2011 |
Keywords
- Laurent expansion in matrix form
- adjoint and determinant derivatives
- matrix polynomial inversion