TY - JOUR
T1 - An inversion formula for a matrix polynomial about a (unit) root
AU - Zoia, Maria
AU - Faliva, Mario
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Laurent expansion in matrix form
KW - adjoint and determinant derivatives
KW - matrix polynomial inversion
KW - Laurent expansion in matrix form
KW - adjoint and determinant derivatives
KW - matrix polynomial inversion
UR - http://hdl.handle.net/10807/5284
U2 - 10.1080/03081081003685936
DO - 10.1080/03081081003685936
M3 - Article
SN - 0308-1087
SP - 541
EP - 556
JO - LINEAR & MULTILINEAR ALGEBRA
JF - LINEAR & MULTILINEAR ALGEBRA
ER -