Greatest common divisor of generalized polynomials and polynomial matrices

DOI10.1016/0024-3795(78)90071-XzbMath0392.15010MaRDI QIDQ1251704

Stephen Barnett, John Maroulas

Publication date: 1978

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Block Companion MatrixBlock Comrade MatrixGeneralized Polynomials and Polynomial MatricesGeneralized Regular Polynomial Matrix AGreatest Common DivisorLinear Control System Theory

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Algebraic methods (93B25) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

The Composition of Polynomials is a Determinant, Polynomials with respect to a general basis. I: Theory, Continued-fraction expansions for ratios of generalized polynomials, Applications of the generalized Sylvester matrix, Polynomials with respect to a general basis. II: Applications, Congenial matrices, Basis-Independent Polynomial Division Algorithm Applied to Division in Lagrange and Bernstein Basis, Computing the Greatest Common Divisor of Polynomials Using the Comrade Matrix, Greatest common divisors from generalized sylvester resultant matrices

Cites Work

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• A companion matrix analogue for orthogonal polynomials
• Greatest common divisor of two polynomials
• Some applications of the comrade matrix
• Applications of the comrade matrix to linear multivariable systems theory
• Matrices, polynomials, and linear time-variant systems