# multi-linear

Let $V_{1},V_{2},\ldots,V_{n},W$ be vector spaces over a field $K$. A mapping

 $M:V_{1}\times V_{2}\times\cdots\times V_{n}\rightarrow W$

is called multi-linear or $n$-linear, if $M$ is linear in each of its arguments.

## Notes.

• A bilinear mapping is another name for a $2$-linear mapping.

• This definition generalizes in an obvious way to rings and modules.

• An excellent example of a multi-linear map is the determinant operation.

Title multi-linear Multilinear 2013-03-22 12:33:05 2013-03-22 12:33:05 rmilson (146) rmilson (146) 10 rmilson (146) Definition msc 15A69 multi-linearity multilinear multilinearity BilinearForm BilinearMap