Zhang, Zhizheng The linear algebra of the generalized Pascal matrix. (English) Zbl 0873.15014 Linear Algebra Appl. 250, 51-60 (1997). This paper is concerned with the “generalized Pascal matrices” \(P_n[x]\), \(Q_n[x]\), \(R_n[x]\) whose \((i,j)\)-entries are \(x^{i-j} {i\choose j}\), \(x^{i+j} {i\choose j}\), \(x^{i+j} {{i+j}\choose j}\) respectively \((i,j=0,1,\dots,n\); \(x\) is a variable). Generalizing results of R. Brawer and M. Pinovino [Linear Algebra Appl. 174, 13–23 (1992; Zbl 0755.15012)], the author expresses \(P_n[n]\) and \(Q_n[x]\) as products of lower unitriangular “summation matrices” and proves the Cholesky factorizations \(R_n[x]= Q_n[x] P_n^T[x]= P_n[x] Q_n^T[x]\). Reviewer: G. E. Wall (Sydney) Cited in 3 ReviewsCited in 56 Documents MSC: 15B36 Matrices of integers 15A23 Factorization of matrices 65F05 Direct numerical methods for linear systems and matrix inversion Keywords:Pascal triangle; generalized Pascal matrices; summation matrices; Cholesky factorizations Citations:Zbl 0755.15012 PDFBibTeX XMLCite \textit{Z. Zhang}, Linear Algebra Appl. 250, 51--60 (1997; Zbl 0873.15014) Full Text: DOI References: [1] Call, G. S.; Velleman, D. J., Pascal’s matrices, Amer. Math. Monthly, 100, 372-376 (1993) · Zbl 0788.05011 [2] Brawer, R.; Pirovino, M., The linear algebra of the Pascal matrix, Linear Algebra Appl., 174, 13-23 (1992) · Zbl 0755.15012 [3] Riordan, J., Combinatorial Identities (1968), Wiley: Wiley New York · Zbl 0194.00502 [4] Stoer, J.; Bulirsch, R., Introduction to Numerical Analysis (1980), Springer-Verlag: Springer-Verlag New York · Zbl 0423.65002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.