A Generalization of ‘PolynomialExtendedGCD’ nd perturbed Sylvester Equations

  Shigeki Matsumoto

faculty of science
Konan University
8-9-1, Okamoto, Kobe, 658-8501


We extend a Mathematica command PolynomialExtendedGCD to the case that the coefficients of polynomials contain indeterminates.  By virtue of such an extension of the command, one can solve the Sylvester (matrix) equation AX – XB = C explicitly even in the case that the square m x m matrix A and n x n matrix B have common eigenvalues, where C is an m x n matrix, X an (unknown) m x n matrix.

The asymptotic behavior (t -> 0) of the solution of perturbed (non-degenarate) Sylvester Equation (A + t ) X - XB = C plays an essential role in our argument.

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