natural basis

A standard basis, also called a natural basis, is a special orthonormal vector basis in which each basis vector has a single nonzero entry with value 1. In n-dimensional Euclidean space R^n, the vectors are usually denoted e_i (or e^⇀_i) with i = 1, ..., n, where n is the dimension of the vector space that is spanned by this basis according to (x_1, x_2, ..., x_n) = x_1 e_1 + x_2 e_2 + ... + x_n e_n. For example, in the Euclidean plane R^2, the standard basis is e_1 | = | e_x = (1, 0) e_2 | = | e_y = (0, 1).

change of basis | orthonormal basis | vector basis | vector space