An inversion formula for a matrix polynomial about a (unit) root

Maria Zoia, Mario Faliva

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

2 Citazioni (Scopus)

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 originaleEnglish
pagine (da-a)541-556
Numero di pagine16
RivistaLINEAR & MULTILINEAR ALGEBRA
DOI
Stato di pubblicazionePubblicato - 2011

Keywords

  • Laurent expansion in matrix form
  • adjoint and determinant derivatives
  • matrix polynomial inversion

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