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multi-linear (Definition)

Let $ V_1, V_2,\ldots, V_n, W$ be vector spaces over a field $ K$. A mapping

$\displaystyle M: V_1\times V_2\times \cdots \times V_n \rightarrow W$
is called multi-linear or $ n$-linear, if $ M$ is linear in each of its arguments.

Notes.



"multi-linear" is owned by rmilson. [ full author list (2) ]
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See Also: bilinear form, bilinear map

Other names:  multi-linearity, multilinear, multilinearity
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Cross-references: operation, determinant, map, modules, rings, obvious, bilinear mapping, arguments, mapping, field, vector spaces
There are 22 references to this entry.

This is version 7 of multi-linear, born on 2002-03-20, modified 2006-09-16.
Object id is 2796, canonical name is Multilinear.
Accessed 10122 times total.

Classification:
AMS MSC: 15A69 (Linear and multilinear algebra; matrix theory :: Multilinear algebra, tensor products)
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