Generalized Pascal Matrices and Their Algebraic Properties
Zhu Chuan-xi · Gongcheng shuxue xuebao · 2010
The algebraic property of Pascal matrices and its generalized forms have wide applications in electronic engineering,combinatorics,fast algorithm,and numerical solutions to differential equations. By means of the basis transformation in polynomial space,a new and simplified proof is presented for the algebraic properties of some generalized Pascal matrices,i.e.,the generalized left Pascal matrices, the generalized right Pascal matrices and the extended generalized Pascal matrices.Moreover,some new algebraic properties of these matrices are given.