\begin{definition}[Definition:Seifert Matrix]
For a knot $K$ with Seifert surface $S$, the '''Seifert matrix''' $V$ of $K$ is defined by its entries as:
:$v_{ij} = \operatorname{lk} \left({ x_i, x_k^* }\right)$
where:
: the $x_a$ are the generators of the fundamental group $\pi_1(S)$
: $x_a^*$ is the positive push-off of $x_a$
: $\operatorname{lk}$ is the linking number of the two loops.
{{NamedforDef|Karl Johannes Herbert Seifert}}
Category:Definitions/Knot Theory
\end{definition}