For what is the theory of determinants? It is an algebra upon algebra; a calculus which enables us to combine and foretell the results of algebraical operations, in the same way as algebra itself enable us to dispense with the performance of the special operations of arithmetic. All analysis must ultimately clothe itself under this form.

The Collected Mathematical Papers of James Joseph Sylvester (Volume 1) - On the Relation Between the Minor Determinants of Linearly Equivalent Quadratic Functions (pp. 246-247), University Press. 1904—1912