An inversion formula for a matrix polynomial about a (unit) root |
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Authors: | Mario Faliva |
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Affiliation: | Department of Mathematics and Econometrics , Catholic University , Largo Gemelli 1, I-20123, Milan, Italy |
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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 the 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. |
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Keywords: | matrix polynomial inversion Laurent expansion in matrix form adjoint and determinant derivatives |
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