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A basis of a vector space is a linearly independent set of vectors that spans . Every vector in can be written uniquely as a linear combination of basis vectors.
Every vector space has a basis (this requires the axiom of choice for infinite-dimensional spaces). All bases of a given vector space have the same cardinality, called the dimension of .
The choice of basis determines the matrix representation of linear maps. Changing the basis changes the matrix but not the underlying map.
@misc{emsenn2026-basis,
author = {emsenn},
title = {Basis},
year = {2026},
url = {https://emsenn.net/library/math/domains/linear-algebra/terms/basis/},
publisher = {emsenn.net},
license = {CC BY-SA 4.0}
}