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1982•Linear and Multilinear AlgebraRequires access

Block partial fraction expansion of a rational matrix

Y.T. Tsay, L.S. Shieh, R.E. Yates, Stephen M. Barnett

Open publisher page 18 citations

Abstract

The main contribution. is a block partial fraction expansion of a rational matrix are polynomial matrices. A new algorithm is derived to construct a transformation matrix that transforms a right (left) solvent to the corresponding left (right) solvent of a matrix polynomial. Also, the algorithm can be used to construct a set of right (left) fundamental matrix polynomials and the inversion of a block Vandermonde matrix. This leads to a new technique to perform the block partial fraction expansion of a class of rational matrices.

About this research paper

What this paper is about

The main contribution. is a block partial fraction expansion of a rational matrix are polynomial matrices. A new algorithm is derived to construct a transformation matrix that transforms a right (left) solvent to the corresponding left (right) solvent of a matrix polynomial. Also, the algorithm can be used to construct a set of right (left) fundamental matrix polynomials and the inversion of a block Vandermonde matrix. This leads to a new technique to perform the block partial fraction expansion of a class of rational matrices.

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OpenAlex reports 18 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

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Available abstract

The main contribution. is a block partial fraction expansion of a rational matrix are polynomial matrices. A new algorithm is derived to construct a transformation matrix that transforms a right (left) solvent to the corresponding left (right) solvent of a matrix polynomial. Also, the algorithm can be used to construct a set of right (left) fundamental matrix polynomials and the inversion of a block Vandermonde matrix. This leads to a new technique to perform the block partial fraction expansion of a class of rational matrices.

Key concepts: Vandermonde matrix, Mathematics, Single-entry matrix, Matrix polynomial, Polynomial matrix, Matrix (chemical analysis), Partial fraction decomposition, Pascal matrix

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