The linear algebra of the pascal matrix

Abstract

AbstractPascal's triangle can be represented as a square matrix in two basically different ways: as a lower triangular matrix Pn or as a full, symmetric matrix Qn. It has been found that the Pn PnT is the Cholesky factorization of Qn. Pn can be factorized by special summation matrices. It can be shown that the inverses of these matrices are the operators which perform the Gaussian elimination steps for calculating Cholesky's factorization. By applying linear algebra we produce combinatorial identities and an existence theorem for diophantine equation systems. Finally, an explicit formula for the sum of the kth powers is given