Standard basis

In mathematics, a standard basis is the natural or canonical basis of a coordinate vector space. Each basis vector has one component equal to 1 and all other components equal to 0. In two and three dimensions, these vectors align with the coordinate directions. Every vector in the space can be expressed uniquely as a linear combination of standard-basis vectors. Standard bases also apply to polynomial and matrix spaces.

Definition

A set of vectors with exactly one component equal to 1 and all remaining components equal to 0.

n-dimensional form

In Rⁿ, it contains n vectors, each with a 1 in one coordinate and 0s elsewhere.

Unique representation

Any vector can be expressed uniquely as a linear combination of these vectors.