The sentence
Although they looked totally inconspicuous at first glance, we knew they are unique and special.
is given. Now, what I though is that "Although they looked totally inconspicuous at first glance," is a subordinate clause and the rest is the main clause. Then I realized that with in the main clause a that is omitted, so that it could read "we knew that they are unique and special." Does this make we knew a matrix clause? Then the two predicator would make sense to me.
The main clause is we knew, as you say.
Technically you could say all subordinate clauses are parts of the main clause, since they function as complements or satellites of the main verb; then the entire sentence is always the main clause. But this is not a very useful analysis, so we normally say the "main clause" excludes its subordinate clauses.
In certain branches of linguistics, a matrix clause is any clause that contains a subordinate clause. That means we knew is also a matrix clause.
