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1Mathematics

A complex number of the form w + xi + yj + zk, where w, x, y, z are real numbers and i, j, k are imaginary units that satisfy certain conditions.*‘Recall that when Hamilton passed from complex numbers to quaternions, multiplication lost one of its normal properties: commutativity.’**‘Two other papers which he published in the same year in publications of the Royal Society of Edinburgh were on the scalar functions of a vector and on an application of quaternions to differential equations.’**‘Hurwitz published a paper on a factorisation theory for integer quaternions in 1896 and applied it to the problem of representing an integer as the sum of four squares.’**‘His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.’**‘Later on, in 1858, Bellavitis included the system of quaternions into his geometric calculus.’*

2rare A set of four people or things.

*‘And when he had apprehended him, he put him in prison, and delivered him to four quaternions of soldiers to keep him; intending after Easter to bring him forth to the people.’**‘I am not likely to attempt your quaternion of colour very soon.’**‘The two figural miniatures and all the canon tables are contained on a separate gathering, a quaternion, physically joined together.’*

**Origin**

Mid 19th century from late Latin quaternio(n-), from Latin quarterni (see quaternary).

**Pronunciation**

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