In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane formed by the pairs (x, y) of real numbers, the standard basis is formed by the vectors Similarly, the standard basis for the three-dimensional space is formed by vectors the scalars vx, vy, vz being the scalar components of the vector v. In the n-dimensional Euclidean space , the standard basis consists of n distinct vectors