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.