Abstract
Relations between the classes of Bézout, Hankel, and Loewner matrices and of their inverses are investigated. All these classes appear as matrix realizations of one operator in suitable bases. Different bases in the space of all polynomials of degree not exceeding n − 1 are considered. These bases correspond to different expansions of the polynomial w(z)p(x) − p(z)w(x) z − x We introduce a matrix K corresponding to this polynomial; this matrix together with its limit forms may be used to represent all the classes of matrices mentioned. In particular we obtain a new interpretation of the variant of generalized Loewner matrices introduced recently by the second-named author.
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