Two methods of treatment have been carried on in parallel lines, the unsymbolic and the symbolic; both of these originated with Cayley, but he with Sylvester and the English school have in the main confined themselves to the former, whilst Aronhold, Clebsch, Gordan, and the continental schools have principally restricted themselves to the latter.
A theory of matrices has been constructed by Cayley in connexion particularly with the theory of linear transformation.
This theorem is due to Cayley, and reference may be made to Salmon's Higher Algebra, 4th ed.
As modified by Cayley it takes a very simple form.
Cayley, however, has shown that, whatever be the degrees of the three equations, it is possible to represent the resultant as the quotient of two determinants (Salmon, l.c. p. 89).