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Polynomial Bézoutian matrix with respect to a general basis. (English) Zbl 0980.15022

The author introduces a class of so-called polynomial Bézoutian matrices. The operator representation relative to a pair of dual bases and the generalized Barnett factorization formula for this kind of matrices are derived. An intertwining relation and generalized Bézoutian reduction via polynomial Vandermonde matrices are presented.

MSC:

15B57 Hermitian, skew-Hermitian, and related matrices
15A54 Matrices over function rings in one or more variables
15A23 Factorization of matrices
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