Multilinear algebra MOC

Tensor

A -tensor on a finite-dimensional vector space is a multilinear object which “eats” covectors and vectors and spits out a scalar. #m/def/linalg/multi Thus a -tensor on is a multilinear map

or equivalently, and element of the tensor product space

In infinite-dimensional contexts, it is necessary to use the latter definition.

Further terminology

• Symmetric tensor
• Antisymmetric tensor

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