Multilinear map

(Redirected from Multilinear)

In linear algebra, a multilinear map is a mathematical function of several vector variables that is linear in each variable.

A multilinear map of n variables is also called a n-linear map.

If all variables belong to the same space, one can consider symmetric, antisymmetric and alternating n-linear maps. The latter coincide if the underlying ring (or field) has a characteristic different from two, else the former two coincide.

Properties

A multilinear map has a value of zero whenever one of its arguments is zero.

For n>1, the only n-linear map which is also a linear map is the zero function, see bilinear map#Examples.

General discussion of where this leads is at multilinear algebra.fr:application multilinéaire

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