Basis function

Monomial basis for Cω The monomial basis for the vector space of analytic functions is given by \{x^n \mid n\in\N\}. This basis is used in Taylor series, amongst others. Monomial basis for polynomials The monomial basis also forms a basis for the vector space of polynomials. After all, every polynomial can be written as a_0 + a_1x^1 + a_2x^2 + \cdots + a_n x^n for some n \in \mathbb{N}, which is a linear combination of monomials. Fourier basis for L2[0,1] Sines and cosines form an (orthonormal) Schauder basis for square-integrable functions on a bounded domain. As a particular example, the collection \{\sqrt{2}\sin(2\pi n x) \mid n \in \N \} \cup \{\sqrt{2} \cos(2\pi n x) \mid n \in \N \} \cup \{1\} forms a basis for L2[0,1]. ==See also==