The nullity of a link, η(L), is equal to the nullity of A + AT where A is a Seifert Matrix of the link. This is also equal to the rank of the two-fold cover of L.

In general, the nullity of a matrix is equal to the dimension of its null space. In the example of L8n6{0,0} below, we can see from the seifert matrix that the nullity of this link is 1.

link diagram seifert matrix seifert matrix
L8n6{0,0} Seifert Matrix of L8n6{0,0} (A) Reduced A+AT L8n6{0,0}

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