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2008•Taiwanese Journal of MathematicsRequires access

ON A SPECIAL GENERALIZED VANDERMONDE MATRIX AND ITS LU FACTORIZATION

Hsuan-Chu Li, Eng-Tjioe Tan

Open publisher page 3 citations

Abstract

We consider a special class of the generalized Vandermonde matrices and obtain an LU factorization for its member by giving closed-form formulae of the entries of $L$ and $U$. Moreover, we express the matrices $L$ and $U$ as products of 1-banded (bidiagonal) matrices. Our result is applied to give the closed-form formula of the inverse of the considered matrix.

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What this paper is about

We consider a special class of the generalized Vandermonde matrices and obtain an LU factorization for its member by giving closed-form formulae of the entries of $L$ and $U$. Moreover, we express the matrices $L$ and $U$ as products of 1-banded (bidiagonal) matrices. Our result is applied to give the closed-form formula of the inverse of the considered matrix.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We consider a special class of the generalized Vandermonde matrices and obtain an LU factorization for its member by giving closed-form formulae of the entries of $L$ and $U$. Moreover, we express the matrices $L$ and $U$ as products of 1-banded (bidiagonal) matrices. Our result is applied to give the closed-form formula of the inverse of the considered matrix.

Key concepts: Vandermonde matrix, Mathematics, Factorization, Inverse, Matrix (chemical analysis), Pure mathematics, Class (philosophy), Algebra over a field

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