Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Scott Kersey
Pages: [1] - [12]
Received Date: October 4, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121725
In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem. In this paper, we extend this result by deriving a formula for the rank of submatrices of the Pascal matrix. Our formula works for both square and non-square submatrices. We also provide bases for the row and column spaces of these submatrices. Further, we apply our result to one-point lacunary polynomial approximation.
rank, Pascal matrix, Birkhoff interpolation.
