It seems easy but I can't prove it. Can anyone give proof or reference?



Why Tristram-Levine signature jumps at the zeros of alexander polynomial?
If $A$ is a Seifert matrix for $K$ and $\omega \in \mathbb{C}$ has norm 1, then the Tristram-Levine signature $\sigma\_\omega(K)$ is the signature of the matrix 


$(1-\omega)A + (1-\bar{\omega})A^T = (1-\bar{\omega})(A^T - \omega A),$


which jumps when some eigenvalue of $A^T - \omega A$ crosses zero (i.e. changes sign). At these values of $\omega$ the product of the eigenvalues, which is $\det(A^T-\omega A) = \Delta\_K(\omega)$, must therefore be zero.


