Document Type
Article
Publication Date
8-27-2016
Publication Title
Journal of Mathematical Sciences: Advances and Applications
DOI
10.18642/jmsaa_7100121709
ISSN
0974-5750
Abstract
The infinite upper triangular Pascal matrix is T = [( j )i] for 0 ≤ i, j. 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 Tr, c comprised of rows r = [r0, … , rm ] and columns c = c0 , … , cm[] of T. We show that Tr, c is invertible r ≤ c i.e., ri ≤ ci for i = 0, …, m(), 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.
Recommended Citation
Kersey, Scott N..
2016.
"Invertibility of Submatrices of the Pascal Matrix and Birkhoff Interpolation."
Journal of Mathematical Sciences: Advances and Applications, 41 (1): 45-56.
doi: 10.18642/jmsaa_7100121709
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/532
Comments
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