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| - | ===== Vector space dimension ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $V$...$\ \mathcal F$-vector space | | ||
| - | | @#FFBB00: $\mathrm{dim}(V)\equiv \mathrm{card}(B)$ | | ||
| - | |||
| - | | @#88DDEE: $B\in\mathrm{basis}(V)$ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | For finite vector spaces, the basis cardinality $\mathrm{dim}(V)$ is the only invariant w.r.t. vector space isomorphisms. | ||
| - | |||
| - | The [[http://en.wikipedia.org/wiki/Zero_vector_space#Vector_space|Zero vector space]] has an empty base. Its [[vector space dimension]] is zero. | ||
| - | ==== Reference ==== | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Vector_space|Vector space]] | ||
| - | ==== Parents ==== | ||
| - | === Equivalent to === | ||
| - | [[Vector space basis]] | ||
