Generalized polynomial bases and the Bézoutian

DOI10.1016/0024-3795(95)00585-4zbMath0873.15016OpenAlexW2046012866MaRDI QIDQ5961704

Robert E. Hartwig, Vaidyanath Mani

Publication date: 26 February 1997

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

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00585-4

zbMATH Keywords

companion matrixHankel matrixcanonical formVandermonde matricesBézout matrix of polynomialshypercompanion matricessimilarity reductionsymmetric bilinear form

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Algebraic methods (93B25) Canonical forms, reductions, classification (15A21)

Related Items

Generalized polynomial Bézoutian with respect to a Jacobson chain basis over an arbitrary field ⋮ Displacement structures and fast inversion formulas for \(q\)-adic Vandermonde-like matrices ⋮ Displacement structure approach to q-adic polynomial-Vandermonde and related matrices ⋮ Polynomial Bézoutian matrix with respect to a general basis ⋮ Basis-Independent Polynomial Division Algorithm Applied to Division in Lagrange and Bernstein Basis ⋮ Displacement structure approach to \(q\)-adic Chebyshev-Vandermonde-like matrices ⋮ Confluent polynomial Vandermonde-like matrices: Displacement structures, inversion formulas and fast algorithm ⋮ Tensored polynomial models

Cites Work

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• Generalizations of the spectral theorem for matrices. II. Matrix polynomials over arbitrary fields
• Resultants, companion matrices, and Jacobson chains
• On Bézoutian reduction with the Vandermonde matrix
• Bézoutian representation via Vandermonde matrices
• Bézoutians
• Duality in polynomial models with some applications to geometric control theory