Arthur Cayley | |
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| Born | 16 August 1821 |
| Died | 26 January 1895 (aged 73) Cambridge, England |
| Education | King's College School |
| Alma mater | Trinity College, Cambridge (BA, 1842) |
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| Scientific career | |
| Fields | Mathematics |
| Institutions | Trinity College, Cambridge |
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Arthur Cayley FRS (/ˈkeɪli/; 16 August 1821 – 26 January 1895) was a British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics, and was a professor at Trinity College, Cambridge for 35 years.
He postulated what is now known as the Cayley–Hamilton theorem—that every square matrix is a root of its own characteristic polynomial, and verified it for matrices of order 2 and 3.[1] He was the first to define the concept of an abstract group, a set with a binary operation satisfying certain laws,[2] as opposed to Évariste Galois' concept of permutation groups. In group theory, Cayley tables, Cayley graphs, and Cayley's theorem are named in his honour, as well as Cayley's formula in combinatorics.
- ^ See Cayley (1858) "A Memoir on the Theory of Matrices", Philosophical Transactions of the Royal Society of London, 148 : 24 : "I have verified the theorem, in the next simplest case, of a matrix of the order 3, ... but I have not thought it necessary to undertake the labour of a formal proof of the theorem in the general case of a matrix of any degree."
- ^ Cayley (1854) "On the theory of groups, as depending on the symbolic equation θn = 1," Philosophical Magazine, 4th series, 7 (42) : 40–47. However, see also the criticism of this definition in: MacTutor: The abstract group concept.