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The dimension of a vector space is the number of elements in any basis. This is well-defined because all bases have the same cardinality.
Two finite-dimensional vector spaces over the same field are isomorphic if and only if they have the same dimension. Dimension is therefore the complete invariant for finite-dimensional vector spaces.
has dimension . The space of polynomials of degree at most has dimension .
@misc{emsenn2026-dimension,
author = {emsenn},
title = {Dimension},
year = {2026},
url = {https://emsenn.net/library/math/domains/linear-algebra/terms/dimension/},
publisher = {emsenn.net},
license = {CC BY-SA 4.0}
}