Memoire on the theory of matrices. In Philosophical Transactions of the Royal Society, Volume 148 (1858), pp. 17-37

Half morocco with gilt lettered spine. Octavo. Fine condition. Although the term "matrix" was introduced into mathematical literature by Sylvester in 1850, the credit for founding the theory of matrices must be given to Arthur cayley, since he published the first expository articles on the subject (Feldman et al., "Arthur Cayley—Founder of Matrix Theory", in The Mathematics Teacher, October, 1962). In this paper Cayley introduces matrices to simplify the notation which arises in simultaneous linear equations. He further introduces the ideas of unit matrix, matrix addition and multiplication, inverse matrix and powers of matrices. More significantly, he introduces the algebraic notation of matrix calculus, explores the non-commutative algebra associated with matrix multiplication and proves the Cayley-Hamilton Theorem—that every matrix satisfies its own characteristic equation. Today the use of matrices in mathematics, physics, engineering and computer science is enormous. (Inventory #: 6944)