@article{e21c360ea3b24f108676851dec2b8790, title = "Binomial matrices", abstract = "Every s x s matrix A yields a composition map acting on polynomials on ℝs. Specifically, for every polynomial p we define the mapping CA by the formula (CAP)(x) := p(Ax), x ∈ ℝs. For each nonnegative integer n, homogeneous polynomials of degree n form an invariant subspace for CA. We let A(n) be the matrix representation of CA relative to the monomial basis and call A(n) a binomial matrix. This paper studies the asymptotic behavior of A(n) as n → ∞. The special case of 2 × 2 matrices A with the property that A2 = I corresponds to discrete Taylor series and motivated our original interest in binomial matrices.", keywords = "Bernstein polynomials, Binomial matrix, De Casteljau subdivision, Homogeneous polynomial, Krawtchouk polynomials, Permanents", author = "Geoff Boyd and Micchelli, {Charles A.} and Gilbert Strang and Ding-Xuan Zhou", year = "2001", doi = "10.1023/A:1012207124894", language = "English", volume = "14", pages = "379--391", journal = "Advances in Computational Mathematics", issn = "1019-7168", publisher = "Springer", number = "4", }