Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Scott Kersey
Pages: [45] - [56]
Received Date: August 27, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121709
The infinite upper triangular Pascal matrix is 
for 
It is easy to see that any leading
principle square submatrix is triangular with determinant 1, hence
invertible. In this paper, we investigate the invertibility of
arbitrary square submatrices 
comprised of rows 
and columns 
of T. We show that is invertible 
or equivalently, iff all diagonal
entries are nonzero. To prove this result, we establish a connection
between the invertibility of these submatrices and polynomial
interpolation. In particular, we apply the theory of Birkhoff
interpolation and Pölya systems.
Pascal matrix, Birkhoff interpolation, Pölya system.
