CAYLEY, Arthur. "Memoir on the Theory of Matrices" and "A Supplementary Memoir on the Theory of Matrices" in Philosophical Transactions of the Royal Society of London, two extracts bound together, as follows: “Matrices” , Vol. 148 (1858), pp. 17- 37; “Supplementary Memoir”, Vol. 156 (1866), pp. 25- 35. Fine condition, bound in beautiful leather and boards of the period, offered with title page and individual title pages for each paper. $850

Cayley (1821-1895) introduced matrices to simplify the solution of simultaneous linear equations, along with matrix functions such as addition and multiplication, and the concepts of matrix calculus.. Cayley is responsible for another branch of algebra over and above invariant theory, the algebra of matrices. The use of determinants in the theory of equations had by his time become a part of established practice, although the familiar square notation...and although their use in geometry, such as was provided by Cayley from the first, was then uncommon. (They later suggested to him the analytical geometry of n dimensions.) Determinants suggested the matrix notation; and yet to those concerned with the history of the “theory of multiple quantity” this notational innovation, even with its derived rules, takes second place to the algebra of rotations and extensions in space (such as was initiated by Gauss, Hamilton, and Grassmann), for which determinant theory provided no more than a convenient language. Cayley’s originality consisted in his creation of a theory of matrices that did not require repeated reference to the equations from which their elements were taken. In his first systematic memoir on the subject ...he established the associative and distributive laws, the special conditions under which a commutative law holds, and the principles for forming general algebraic functions of matrices. He later derived many important theorems of matrix theory. Thus, for example, he derived many theorems of varying generality in the theory of those linear transformations that leave invariant a quadratic or bilinear form. Notice that since it may be proved that there are n(n + 1)/2 relations between them, Cayley expressed the n2 coefficients of the nary orthogonal transformation in terms of n(n - 1)/2 parameters. His formulas, however, do not include all orthogonal transformations except as limiting cases .”--Complete Dictionary of Scientific Biography, online.

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