The matrices of Pascal and other greats

Abstract

The Pascal matrix has been known since ancient times,and it was mentioned in Chinese mathematical texts dating from 1303. Nevertheless, it has been studied carefully only recently. It arises in probability, numerical analysis,surface reconstruction, combinatorics; we came across it while studying stability properties of numerical methods for solving ordinary differential equations. Our goal is to share some of the beauty of the Pascal matrix and show how it is related to other matrices associated with great names such as Vandermonde, Frobenius, Stirling,etc