Arthur Cayley

Arthur Cayley , 1821-95, English mathematician. He was admitted to the bar in 1849. In 1863 he was appointed first Sadlerian professor of mathematics at Cambridge. His researches, which covered the field of pure mathematics, included especially the theory of matrices and the theory of invariants. The algebra of matrices was the tool Heisenberg used in 1925 for his revolutionary work in quantum mechanics. The concept of invariance is important in modern physics, particularly in the theory of relativity. Cayley's collected papers were published in 13 volumes (1889-98).

Cayley table (composition table; operation table) A tabular means of describing a finite group, first used by the 19th-century mathematician Arthur Cayley. To illustrate, the set {1,–1,i,–i}

forms a group under the dyadic operation ◦ as described by the Cayley table shown in the diagram. The value of –1◦i, for example, is –i. The name composition table is usually used when the group operation is composition of functions.