multi-linearMultilinear2002-03-20 22:12:502006-09-16 13:46:09Definition\usepackage{amsmath}
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\newtheorem{proposition}{Proposition}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 {\em multi-linear} or $n$-linear, if $M$ is linear in each of
its arguments.
\paragraph{Notes.}
\begin{itemize}
\item A bilinear mapping is another name for a $2$-linear mapping.
\item This definition generalizes in an obvious way to rings and
modules.
\item An excellent example of a multi-linear map is the determinant operation.
\end{itemize}