In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as \mathbb{R}^n or \mathbb{C}^n) is the set of vectors, each of whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane \mathbb{R}^2 formed by the pairs (x, y) of real numbers, the standard basis is formed by the vectors
:\mathbf{e}_x = (1,0),\quad \mathbf{e}_y = (0,1).
Similarly, the standard basis for the three-dimensional space \mathbb{R}^3 is formed by vectors
:\mathbf{e}_x = (1,0,0),\quad \mathbf{e}_y = (0,1,0),\quad \mathbf{e}_z=(0,0,1).
Here the vector ex points in the x direction, the vector ey points in the y direction, and the vector ez points in the z direction. There are several common notations for standard-basis vectors, including {ex, ey, ez}, {e1, e2, e3}, {i, j, k}, and {x, y, z}. These