Tensor product of vector spaces ↩

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created: 2021-12-04 17:20:08
modified: 2022-01-11 16:02:47

and vector spaces over the same field .
Then is the tensor product of these vector spaces.

Elements

Algebraically, the vector space is spanned by elements of the form (Outer product) and the following rules are satisfied :

A basic consequence is that .

Basis

A vector basis of of and of gives a basis for , namely for all pairs .

Dimension

If is dimensional and is dimensional, then has dimension .

Examples

See also