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Tensor Space


Let E be a linear space over a field K. Then the vector space tensor product  tensor _(lambda=1)^(k)E is called a tensor space of degree k. More specifically, a tensor space of type (r,s) can be described as a vector space tensor product between r copies of vector fields and s copies of the dual vector fields, i.e., one-forms. For example,

 T^((3,1))=TM tensor TM tensor TM tensor T^*M

is the vector bundle of (3,1) tensors on a manifold M. Tensors of type (r,s) form a vector space.


See also

Tensor, Vector Space

Portions of this entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd and Weisstein, Eric W. "Tensor Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TensorSpace.html

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