‎"CAYLEY, ARTHUR. - THE CAYLEY-HAMILTON THEOREM ANNOUNCED - THE MATHEMATICS OF QUANTUM MECHANICS.‎
‎A Memoir on the Theory of Matrices. Received December 10, 1857, - Read January 14, 1858. (+) A Supplementary Memoir on the Theory of Matrices. Received October 24, - Read December 7, 1865.‎

‎(London, Richard Taylor and William Francis, 1858 and Taylor and Francis, 1866. 4to. No wrappers as extracted from ""Philosophical Transactions"" Vol. 148 - Part I. Pp. 17-37, and Vol. 156 - Part I, Pp. 25-35. Clean and fine.‎

Reference : 42295

‎First appearance of this outstanding contribution to mathematics, announcing his invention and developments of the ALGEBRA OF MATRICES, what is now called the Cayley-Hamilton theorem for square matrices of any order. ""The subject originated in a memoir of 1858 (the paper offered) and grew directly out of simple observations on the way in which the transformations (linear) of the theory of algebraic invariants are combined...a distinctive feature of these rules is that multiplication is not commutative...we get different results according to the order in which we do the multiplication... (it) seems about as far from anything of scientific or practical use as anything could possible be. Yet sixty seven years after Cayley's invented it, HEISENBERG in 1925 recognized in the algebra of matrices exactly the tool which he neede for his revolutionary work in QUANTUM MECHANICS.""(Bell, Men of Mathematics).""It was in connection with the study of invariants under linear transformation that Cayley first introduced matrices to simplify the notation involved. Here he gave some basic notions. This was followed by his first major paper on the subject ""A Memoir on the Theory of Matrices."", the paper offered here. (Kline, Mathematical Thought...p. 806).‎