Using Riordan arrays, we introduce a generalized Delannoy matrix by weighted Delannoy numbers. It turn out that Delannoy matrix, Pascal matrix, and Fibonacci matrix are all special cases of the generalized Delannoy matrices, meanwhile Schröder matrix and Catalan matrix also arise in involving inverses of the generalized Delannoy matrices. These connections are the focus of our paper. The half o...

A scaled version of the lower and the upper triangular factors of the inverse of the Vandermonde matrix is given. Two applications of the q-Pascal matrix resulting from the factorization of the Vandermonde matrix at the q-integer nodes are introduced. c © 2007 Elsevier Ltd. All rights reserved.

In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices, such as the Stirling matrices of both kinds, the Lah matrix, and the generalized Pascal matrix. To make the results more general, the discussion is also extended to the generalized Fibonacci numbers and the corresponding matrix. Moreover, ba...

We study the properties of a parameterized family of generalized Pascal matrices, defined by Riordan arrays. In particular, we characterize the central elements of these lower triangular matrices, which are analogues of the central binomial coefficients. We then specialize to the value 2 of the parameter, and study the inverse of the matrix in question, and in particular we study the sequences ...

The LDI matrix is introduced in its full and shortened forms. As an analogy of the Pascal matrix for the bilinear transform, the LDI matrix serves to transform the coefficients of the transfer functions of continuousand discrete-time linear circuits which are connected by the LDI (Lossless Discrete Integration) transform. The basic properties of the LDI matrix are presented and a procedure of i...

We define a new generalization of Gaussian Pell-Lucas polynomials. call it $d-$Gaussian Then we present the generating function and Binet formula for give matrix representation Using Riordan method, obtain factorizations Pascal involving

for 0 ≤ i, j ∈ N. The matrix P is hence the famous Pascal triangle yielding the binomial coefficients and can be recursively constructed by the rules p0,i = pi,0 = 1 for i ≥ 0 and pi,j = pi−1,j + pi,j−1 for 1 ≤ i, j. In this paper we are interested in (sequences of determinants of finite) matrices related to P . The present section deals with determinants of some minors of the above Pascal tria...

An elimination procedure based on Schur complement calculation is proposed for restoring the nonzero elements of a sparse Jacobian matrix. We provide a sparsity usage parameter that can be specified by users to tune the cost of matrix-vector product calculation and the cost of restoration of the nonzero entries. We employ Pascal seeding to compress the Jacobian matrix. Preliminary numerical tes...