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algebra > multilinear algebra > multilinear map

Preferred term

multilinear map

Definition(s)

In linear algebra, a multilinear map is a function of several variables that is linear separately in each variable. More precisely, a multilinear map is a function

${\\displaystyle f\\colon V_{1}\ imes \\cdots \ imes V_{n}\ o W{\ ext{,}}}$

where ${\\displaystyle V_{1},\\ldots ,V_{n}}$ and ${\\displaystyle W}$ are vector spaces (or modules over a commutative ring), with the following property: for each ${\\displaystyle i}$ , if all of the variables but ${\\displaystyle v_{i}}$ are held constant, then ${\\displaystyle f(v_{1},\\ldots ,v_{i},\\ldots ,v_{n})}$ is a linear function of ${\\displaystyle v_{i}}$ .

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Multilinear_map)

Broader concept(s)

multilinear algebra

Narrower concept(s)

Synonym(s)

multilinear mapping

In other languages

application multilinéaire

French

URI

http://data.loterre.fr/ark:/67375/PSR-S7M9JFHC-2

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