Definition:Seifert Matrix

Definition
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.