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'multi-linear'
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| Title of object: |
multi-linear |
| Canonical Name: |
Multilinear |
| Type: |
Definition |
| Created on: |
2002-03-20 22:12:50-05 |
| Modified on: |
2002-04-10 13:37:48-04 |
| Classification: |
msc:15A69 |
| Synonyms: |
multi-linear=multi-linearity |
Preamble:
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Content:
Let $V_1, V_2,\ldots, V_n, W$ be vector spaces over a field $K$. A
mapping $$M: V_1\times V_2\times \ldots \times V_n \rightarrow W$$ 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} |
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