TITLE: What are the possible linking matrices of a quasi-positive link?
QUESTION [10 upvotes]: I was surprised recently to come across a 3-component link where the linking number of two of the components was negative. For a while I thought I had made a mistake, then I thought a little more and realized that there was no particular reason that the linking numbers had to be all positive.
The linking matrix I found was
$$\begin{pmatrix} * & 3 & 3 \\ 3 & * & -1 \\ 3 & -1 & * \end{pmatrix}.
$$
Here is the link. (I haven't attempted to find a quasi-positive representative yet, the proof it's quasi-positive was pretty indirect.)

REPLY [2 votes]: Any linking matrix appears as linking matrix of a strongly quasipositive link.
This follows from a result of Rudolph ("Constructions of Quasipositive Knots and Links, I") that any Seifert matrix appears as Seifert matrix of a strongly quasipositive link.