Rank of Submatrices of the Pascal Matrix

Scott N. Kersey

doi:10.18642/jmsaa_7100121725

Rank of Submatrices of the Pascal Matrix

Scott N. Kersey

Mathematical Sciences

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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.

Original language	American English
Journal	Journal of Mathematical Sciences: Advances and Applications
Volume	42
DOIs	https://doi.org/10.18642/jmsaa_7100121725
State	Published - Oct 4 2016

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Education
Mathematics

Keywords

Pascal Matrix
Rank
Submatrices

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https://arxiv.org/abs/1702.03194

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title = "Rank of Submatrices of the Pascal Matrix",

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N2 - 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.

AB - 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.

KW - Pascal Matrix

KW - Rank

KW - Submatrices

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/533

U2 - 10.18642/jmsaa_7100121725

DO - 10.18642/jmsaa_7100121725

M3 - Article

VL - 42

JO - Journal of Mathematical Sciences: Advances and Applications

JF - Journal of Mathematical Sciences: Advances and Applications

ER -

Rank of Submatrices of the Pascal Matrix

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