In terms of function, a matrix clause determines the central situation of a sentence.
Examples and Observations:
- "In discussing subordination, it is common to find contemporary linguists using the terms matrix clause and embedded clause. It is important to understand how these terms relate to more familiar ones. A matrix clause is a clause that contains another clause. Thus, the main clause in (37), the professor told the students, is a matrix clause since it contains another clause (that he was going to cancel the next class), which is said to be embedded inside the matrix clause:
(37). . . The matrix clause determines the central situation of the construction. It casts its syntactic and semantic 'shadow,' as we might say, over the situation described by the clause that follows. So the situation described in the embedded clause is contained by, and functions as an element of, the situation described by the matrix clause."
The professor told the students that he was going to cancel the next class.
(Martin J. Endley, Linguistic Perspectives on English Grammar. Information Age, 2010)
- "A matrix clause is often a main clause . . ., but it need not be: it can itself be a subordinate clause. In the sentence The victim told police that the man who attacked her had had a beard, the subordinate clause who attacked her is contained within the subordinate clause that the man . . . had had a beard."
(R.L. Trask, Dictionary of English Grammar. Penguin, 2000)
- "[S]ubordination . . . is where one clause (the subordinate clause) is somehow less important than the other (the matrix clause). There are three types of subordination: complementation, relative clauses, and adverbial subordination.
"Complement clauses are those clauses which substitute for a noun phrase in a sentence. For example, in English we can say I saw the boy, with the boy the object of the verb saw. But we can also say I saw (that) the boy left, I saw the boy leave, and I saw the boy leaving. In each case, where we might expect a noun phrase like the boy, we have a whole clause, with at least a subject and a verb. Which type of complement clause we get depends on the verb in the matrix clause, so that with want rather than see, we can have I wanted the boy to leave, but not *I wanted the boy left or *I wanted the boy leaving. . . .
"Relative clauses add some extra information about a noun phrase in a sentence, and in English often begin with who, which or that--the man who gave me the book left contains the relative clause who gave me the book . . ..
"The third type of subordination, adverbial subordination, covers those subordinate clauses which are similar in use to adverbs . . .."
(A. Davies and C. Elder, The Handbook of Applied Linguistics. Wiley-Blackwell, 2005)
- Matrix Subjects and Matrix Verbs
"(17) a. Mary wondered [whether Bill would leave]. . . .
"The clause of which the subordinate clause is a constituent, such as Mary wondered whether Bill would leave in (17a), is referred to as the higher clause or the matrix clause. The topmost clause in a complex structure is the main clause, or the root clause. The verb of the matrix clause can be referred to as the matrix verb; the subject of the matrix clause can be referred to as the matrix subject. In (17a) wondered is the matrix verb and Mary is the matrix subject. The verb of the embedded clause can be referred to as the embedded verb; the subject of the embedded clause can be referred to as the embedded subject. In (17a) leave is the embedded verb and Bill is the embedded subject."
(Liliane Haegeman and Jacqueline Guéron, English Grammar: A Generative Perspective. Blackwell, 1999)