According to Lickorishs book (Introduction to Knot Theory) I know that $|H_1(X;Z)| =$ order of the group $ H_1(X;Z) = |det(A+A^t)|$, where X is the double cover of $S^3$ branched over a link L and A is the Seifert Matrix for L.
However, Lipsons Paper (An evaluation of a link polynomial) states that the nullity of this matrix $A+A^t$ is equal to $dim(H_1(X;Z))$. This is not clear to me at all and I would be very happy if someone could explain to me why this is true or give me a reference where this can be read. Thank you very much in advance!