multilinear

Adjective

Meaning

Having many lines.

Having many linear aspects.

(mathematics, of a function etc) That is linear in each variable separately.

Synonyms

Phrases with the word

Examples

Moreover, such an array can be realized as the components of some multilinear map T. This motivates viewing multilinear maps as the intrinsic objects underlying tensors. Source: Internet

Moreover, the universal property of the tensor product gives a 1 -to- 1 correspondence between tensors defined in this way and tensors defined as multilinear maps. Source: Internet

However, it may be convenient for notation to consider n-ary functions, as for example multilinear maps (which are not linear maps on the product space, if n≠1). Source: Internet

But, because T is linear in all of its arguments, the components satisfy the tensor transformation law used in the multilinear array definition. Source: Internet

They can be thought of as alternating, multilinear maps on k tangent vectors. Source: Internet

This follows from properties 7 and 9 (it is a general property of multilinear alternating maps). Source: Internet

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