Given a Seifert form 
, choose a basis 
, ..., 
for 
as a 
-module so every element is uniquely expressible as
 |
(1)
|
with 
integer. Then define the Seifert matrix 
as the 
integer matrix
with entries
 |
(2)
|
For example, the right-hand trefoil knot has Seifert matrix
![V=[-1 1; 0 -1].](/images/equations/SeifertMatrix/NumberedEquation3.svg) |
(3)
|
A Seifert matrix is not a knot invariant, but it can be used to distinguish between different Seifert surfaces for a given knot.
