Given a Seifert surface F of a knot K in S^{3}, take a_{1},
a_{2}, ..., a_{n} to be a basis for the first homology group of F.
Then the i,j entry of the Seifert matrix is obtained by taking the linking number of a_{i} &
a_{j}^{#}, where a_{j}^{#} indicates a copy of
the curve a_{j} which has been pushed slightly off F in the positive normal direction.

Though not itself an invariant of knots, the Seifert matrix can be used to compute knot invariants such as signature, Alexander polynomial, and determinant.