nLab Arthur Cayley

Arthur Cayley (16 August 1821 – 26 January 1895) is one of the principal and most prolific mathematicians of 19-th century, especially in algebra. He also worked on questions in algebraic geometry, graph theory …

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Selected writings

Introducing the octonions:

• Arthur Cayley, On certain results relating to quaternions, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science Series 3 Volume 26, 1845 - Issue 171 (doi:10.1080/14786444508562684)

Cayley’s 1848 paper on elimination theory contains probably the first serious application of homological algebra, including Koszul complexes. It is reproduced and commented in the book

• I. M. Gelfand, M. M. Kapranov, A. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Birkhäuser 1994, 523 pp.

Introducing matrices and matrix calculus:

• Arthur Cayley: A Memoir on the Theory of Matrices, Philosophical Transactions of the Royal Society of London, 148 (1858) 17-37 [jstor:108649]

Related entries

• resultant

• hyperdeterminant

• Cayley form

• weak Cayley table

• Cayley-Hamilton theorem

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