Expansion and Factorization of Three Special Matrices UsingStirling Numbers

In this paper we introduce the Pascal, Stirling and Vandermonde matrices of one and two variables. It is shownthat these matrices can be obtained from the Stirling numbers of the first kind s(n, k) and of the second kindS(n, k) . Also the factorization and LDU factorization of the Stirling and Vandermonde matrices are obtainedusing Pascal and some special matrices.AMS classification: 15-xx ; 33-xx

Keywords:

Stirling numbers , Pascal matrix , Stirling matrix , Vandermonde matrix , LDU factorization