LDU decomposition of an extension matrix of the Pascal matrix

Abstract: Let denote a set of all elements of weighted lattice paths with weight in the xy-plane from to such that a vertical step , a horizontal step , and a diagonal step are endowed with weights , and respectively and let denote the weight of defined bywhere is the product of the weights of all its steps in . A matrix is called a lattice path matrix with weight if for a triple , and of real numbers . In this paper, we present LDU decomposition of lattice path matrices with weight and related properties for every triple , and of real numbers, and a necessary and sufficient condition in which the symmetric lattice path matrices are positive definite. We also investigate the relationship between the lattice path matrices and generalized Pascal matrices. [Copyright &y& Elsevier]