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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.’
‘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.’
‘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.’
‘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.’
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).