Meaning of quaternion in English:


Pronunciation /kwəˈtəːnɪən/


  • 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.’
  • 2 rare 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.’


Middle English (in sense quaternion (sense 2)): from late Latin quaternio(n-), from Latin quarterni (see quaternary).