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An extension of Vandermonde's determinant

Kimball Martin, J. M. Olazábal

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Abstract

Let D be an integer domain and D[x 1,..., x r] the ring of polynomials in r variables over D. In this note, we consider a matrix over D[x 1, ..., x r], inspired by the Lagrange‐Sylvester Interpolation, which is an extension of Vandermonde's matrix, and we compute its determinant. The formula obtained includes the well known Vandermonde's determinant.

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What this paper is about

Let D be an integer domain and D[x 1,..., x r] the ring of polynomials in r variables over D. In this note, we consider a matrix over D[x 1, ..., x r], inspired by the Lagrange‐Sylvester Interpolation, which is an extension of Vandermonde's matrix, and we compute its determinant. The formula obtained includes the well known Vandermonde's determinant.

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Available abstract

Let D be an integer domain and D[x 1,..., x r] the ring of polynomials in r variables over D. In this note, we consider a matrix over D[x 1, ..., x r], inspired by the Lagrange‐Sylvester Interpolation, which is an extension of Vandermonde's matrix, and we compute its determinant. The formula obtained includes the well known Vandermonde's determinant.

Key concepts: Vandermonde matrix, Mathematics, Extension (predicate logic), Matrix (chemical analysis), Integer (computer science), Combinatorics, Interpolation (computer graphics), Lagrange polynomial

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