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We consider a certain class of 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 and give a general formula for their determinants when the corresponding polynomial has degree . As an immediate consequence, we deduce linear independence of sets of translations and scalings of a polynomial under suitable assumptions.
Cheney, E. W., and Light, W. A. (2009). A Course in Approximation Theory. Providence, R. I.: American Mathematical Society.
Lee, C., and Peterson, V. (2014). The Rank of Recurrence Matrices. College Mathematics Journal, 45 (3), p. 207 – 215.
Mirsky, L. (1990). An Introduction to Linear Algebra. Reprint of the 1972 edition. New York, N. Y.: Dover Publications, Inc.
Tao, T. (2012). Topics in Random Matrix Theory. Providence, R. I.: American Mathematical Society.
Yandl, A. L., and Swenson, C. (2012). A Class of Matrices with Zero Determinant. Mathematics Magazine, 85 (2), p. 126 – 130.