Dimension (vector space) | Wikipedia audio article
Channel: Subhajit Sahu
Date: 27/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Dimension_(vector_space)


00:00:56 1 Examples
00:01:42 2 Facts
00:02:08 3 Generalizations
00:02:33 3.1 Trace
00:03:01 4 See also
00:05:00 5 Notes
00:05:04 6 References
00:05:48 7 External links
00:09:49 See also



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SUMMARY
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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. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension.
For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined. We say V is finite-dimensional if the dimension of V is finite, and infinite-dimensional if its dimension is infinite.
The dimension of the vector space V over the field F can be written as dimF(V) or as [V : F], read "dimension of V over F". When F can be inferred from context, dim(V) is typically written.