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## Thursday, April 24, 2008

### The differentiation matrix for arithmetic polynomials

#### 1 comment:

1. Absolutely. First, notice that the space of polynomials (infinite dimensional, of course), call it V, forms a vector space over your base field, say the field K. Let V(n) be the subspace of V consisting of polynomials of degree <= n. Define differentiation on V(n) in the usual sense. Then differentiation becomes a linear operator on V(n), call it D. Now, V(n) is finite dimensional (of dimension n + 1), so the matrix representation of D is (n + 1)x(n + 1), and will handle any polynomial in V(n).

Cheers!

William

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