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 -dimensional Euclidean space , the vectors are usually denoted (or ) with , ..., , where is the dimension of the vector space that is spanned by this basis according to

For example, in the Euclidean plane , the standard basis is

Similarly, for Euclidean 3-space , the standard basis is

See also

Change of Basis, Orthonormal Basis, Vector Basis, Vector Space

Portions of this entry contributed by Al Roth

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Cite this as:

Weisstein, Eric W., with contributions by Al Roth. "Standard Basis." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StandardBasis.html

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