The matrix clause of °subordinate clause is the minimal clause that contains it.
A matrix-clause fragment is the part of a matrix clause that is not the subordinate clause (Haspelmath 2020). In many cases, linguists actually mean a matrix-clause fragment when they use the term "matrix clause". (Another term that is frequently used in the same sense is "main clause", but a main clause is expected to be non-subordinate, in contrast to a matrix clause, which can itself be subordinate.)
matrix clause (CXN) = the clause in a complex sentence construction that also contains a dependent clause; the dependent clause is a dependent of the matrix clause. Example: in She watered the plants before she ate lunch, She watered the plants is an instance of a matrix clause; before she ate lunch is a dependent clause. A matrix clause is often, but not always, a main clause; it may be a subordinate clause that is itself dependent on another matrix clause.