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linear algebra

Source: miklos schweitzer 2011 q5

August 29, 2021
linear algebrapolynomial

Problem Statement

Let n, k be positive integers. Let fa(x):=∣∣x−a∣∣2nf_a(x) := ||x - a||^{2n} , where the vectors x=(x1,...,xk),a∈Rkx = (x_1, ..., x_k) , a\in R^k , and ||·|| is the Euclidean norm. Let the vector space Qn,kQ_{n, k} be generated by the functions faf_a (a∈Rka\in R^k). What is the largest integer N for which Qn,kQ_{n, k} contains all polynomials of x1,...,xkx_1, ..., x_k whose total degree is at most N?
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