Inverting linear combinations of identity and generalized Catalan matrices

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• 作者：Predrag Stanimirović ; Stefan Stanimirović
• 关键词：Catalan number ; Generalized Catalan number ; Catalan matrix ; Generalized Catalan matrix ; Generalized hypergeometric function ; Matrix inverse ; Hadamard product
• 刊名：Linear Algebra and its Applications
• 出版年：2010
• 出版时间：1 December 2010
• 年：2010
• 卷：433
• 期：7
• 页码：1472-1480
• 全文大小：171 K

文摘

We introduce the notion of the generalized Catalan matrix as a kind of lower triangular Toeplitz matrix whose nonzero elements involve the generalized Catalan numbers. Inverse of the linear combination of the Pascal matrix with the identity matrix is computed in Aggarwala and Lamoureux (2002) [1]. In this paper, continuing this idea, we invert various linear combinations of the generalized Catalan matrix with the identity matrix. A simple and efficient approach to invert the Pascal matrix plus one in terms of the Hadamard product of the Pascal matrix and appropriate lower triangular Toeplitz matrices is considered in Yang and Liu (2006) [14]. We derive representations for inverses of linear combinations of the generalized Catalan matrix and the identity matrix, in terms of the Hadamard product which includes the Generalized Catalan matrix and appropriate lower triangular Toeplitz matrix.