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vector_space_dimension [2013/08/31 16:15] nikolaj |
vector_space_dimension [2013/08/31 16:30] nikolaj |
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| ==== Discussion ==== | ==== Discussion ==== | ||
| - | The basis cardinality $\mathrm{dim}(V)$ is the only invariant w.r.t. vector space isomorphisms. | + | For finite vector spaces, the basis cardinality $\mathrm{dim}(V)$ is the only invariant w.r.t. vector space isomorphisms. |
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| + | 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 ==== | ==== Reference ==== | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Vector_space|Vector space]] | Wikipedia: [[http://en.wikipedia.org/wiki/Vector_space|Vector space]] | ||
