Journal of Mathematical Sciences: Advances and Applications
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.
Kersey, Scott N..
"Rank of Submatrices of the Pascal Matrix."
Journal of Mathematical Sciences: Advances and Applications, 42 (1): 1-12.
doi: 10.18642/jmsaa_7100121725 source: http://scientificadvances.co.in/admin/img_data/1102/images/JMSAA7100121725ScottKersey.pdf