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 $$x_a \ $$, and $$\operatorname{lk} \ $$ is the linking number of the two loops.