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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.
‘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.’
‘Later on, in 1858, Bellavitis included the system of quaternions into his geometric calculus.’
‘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.’
‘His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.’
‘Recall that when Hamilton passed from complex numbers to quaternions, multiplication lost one of its normal properties: commutativity.’
2rare A set of four people or things.
‘I am not likely to attempt your quaternion of colour very soon.’
‘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.’
‘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).