Two Pascal Matrices

Dr. Peter Gibson

Department of Mathematical Sciences
University of Alabama in Huntsville

October 15, 2004
202 Madison Hall
3:00 PM (Coffee and Cookies at 2:30)

Abstract

A well-known way to generate the binomial coefficients is to utilize the Pascal triangle. A number of matrices that use the entries from this triangle have been introducted over the years. In this talk properties of two such Pascal matrices are discussed. One of these matrices is the n × n upper triangular matrix U n u i j with

u i j 1 i 1 ( j 1 i 1 ) ,  1 i j n

and the other one is the n × n symmetric matrix S n s i j with

s i j s j i ( i j 2 i 1 ) ,  i,j 1 2 ... n