On Determinants of Matrices Generated From Values of Polynomials

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On Determinants of Matrices Generated From Values of Polynomials
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Published: Aug 30, 2022
Keywords:
Vandermonde matrix, Determinant, Polynomial interpolation

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Thanawat Palakawong
Chonradsadornumrung School, Chonburi, 20000
Detchat Samart
Department of Mathematics, Faculty of Science, Burapha University, Chonburi, 20131

Abstract

We consider a certain class of gif.latex?n\times&space;n matrices whose elements are given by values of polynomials. We show that their determinants vanish if the degree of the  corresponding polynomial does not exceed gif.latex?n-2 and give a general formula for their determinants when the corresponding polynomial has degree gif.latex?n-1. As an immediate consequence, we deduce linear independence of sets of translations and scalings of a polynomial under suitable assumptions.

Article Details

How to Cite
Palakawong, T., & Samart, D. (2022). On Determinants of Matrices Generated From Values of Polynomials. Mathematical Journal by The Mathematical Association of Thailand Under The Patronage of His Majesty The King, 67(707), 1–12. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/245236
Issue
Vol. 67 No. 707 (2022): May – August 2022
Section
Research Article

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