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2006•Journal of Mathematical Research and ExpositionRequires access

On a Relationship between Pascal Matrix and Vandermonde Matrix

Sheng-Liang Yang

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Abstract

EI-Mikkawy M obtained that the symmetric Pascal matrix Q_n and the Vandermonde matrix V_n are connected by the equation Q_n = T_nV_n, where T_n is a stochastic matrix in. In this paper, a decomposition of the matrix T_n is given via the Stirling matrix of the first kind, and a recurrence relation of the elements of the matrix T_n is obtained, so an open problem proposed by EI-Mikkawy is solved. Some combinatorial identities are also given.

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What this paper is about

EI-Mikkawy M obtained that the symmetric Pascal matrix Q_n and the Vandermonde matrix V_n are connected by the equation Q_n = T_nV_n, where T_n is a stochastic matrix in. In this paper, a decomposition of the matrix T_n is given via the Stirling matrix of the first kind, and a recurrence relation of the elements of the matrix T_n is obtained, so an open problem proposed by EI-Mikkawy is solved. Some combinatorial identities are also given.

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Available abstract

EI-Mikkawy M obtained that the symmetric Pascal matrix Q_n and the Vandermonde matrix V_n are connected by the equation Q_n = T_nV_n, where T_n is a stochastic matrix in. In this paper, a decomposition of the matrix T_n is given via the Stirling matrix of the first kind, and a recurrence relation of the elements of the matrix T_n is obtained, so an open problem proposed by EI-Mikkawy is solved. Some combinatorial identities are also given.

Key concepts: Vandermonde matrix, Pascal matrix, Mathematics, Matrix function, Matrix (chemical analysis), Centrosymmetric matrix, Pascal (unit), Nonnegative matrix

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