Article
Rank of Submatrices of the Pascal Matrix
Journal of Mathematical Sciences: Advances and Applications
Document Type
Article
Publication Date
10-4-2016
DOI
10.18642/jmsaa_7100121725
Disciplines
- Education and
- Mathematics
Abstract
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.
Citation Information
Scott N. Kersey. "Rank of Submatrices of the Pascal Matrix" Journal of Mathematical Sciences: Advances and Applications Vol. 42 Iss. 1 (2016) p. 1 - 12 ISSN: 0974-5750 Available at: http://works.bepress.com/scott_kersey/30/
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