Multilinear function

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

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 ${\displaystyle f(v_{1},\ldots ,v_{n})}$ is a linear function of ${\displaystyle v_{i}}$.

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