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Dimension (vector space)
Number of vectors in any basis of the vector space / From Wikipedia, the free encyclopedia
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In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field.[1][2] It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension.
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For every vector space there exists a basis,[lower-alpha 1] and all bases of a vector space have equal cardinality;[lower-alpha 2] as a result, the dimension of a vector space is uniquely defined. We say is finite-dimensional if the dimension of
is finite, and infinite-dimensional if its dimension is infinite.
The dimension of the vector space over the field
can be written as
or as
read "dimension of
over
". When
can be inferred from context,
is typically written.