\begin{definition}[Definition:Interior Multiplication]
Let $V$ and $V^*$ be a vector space and its dual.
Let $\omega \in \map {\Lambda^k} {V^*}$ be an alternating $k$-tensor.
Let $v \in V$ be a vector.
Let $v\, \lrcorner\, \omega$ be an alternating $\paren {k - 1}$-tensor such that:
:$\map {\paren {v\, \lrcorner\, \omega}} {w_1, \ldots, w_{k - 1}} := \map \omega {v, w_1, \ldots, w_{k - 1}}$
Then the mapping $\omega \mapsto v\, \lrcorner\, \omega$ is known as the '''interior multiplication by $v$'''.
If $\omega$ is a $0$-tensor then:
:$v\, \lrcorner\, \omega := 0$
\end{definition}