Dimension of a vector space ( $dim V$ )

The dimension of a vector space is the cardinality of any of its bases.

Table of contents
- Finite-dimensional vector space Dimension of a vector space
- Infinite-dimensional vector space Dimension of a vector space

Finite-dimensional vector space

A vector space is finite-dimensional when it has a finite set as a basis.

Infinite-dimensional vector space

An infinite-dimensional vector space has no finite basis, so its dimension is an infinite cardinal.

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