biquaternionn.
/bʌɪkwɒˈtəːnɪən/ Mathematics.
1. A quaternion with complex coefficients.
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quaternion1844
biquaternion1852
1852 Rep. Brit. Assoc. (1853) Notices & Abstracts 2 On Biquaternions. By Sir William R. Hamilton.
1853 W. R. Hamilton Lect. Quaternions p. lxviii A biquaternion may be considered generally as the sum of a biscalar and a bivector.
1905 C. J. Joly Man. Quaternions ii. 21 The tensor of a biquaternion may vanish.
2. (See quots.)
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the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > quaternion > two of
biquaternion1873
1873 W. K. Clifford in Proc. London Math. Soc. 4 386 In this way the ratio γ+ωδ/ α+ωβ is expressed in the form q + ωr, which expression may conveniently be called a biquaternion.
1876 W. K. Clifford Math. Papers (1882) 394 The ratio of two motors is a quantity of the form..s + ωt (if 2s = p + q, t = 2p − q), where p, q, s, t are quaternions. This combination of two quaternions I have called a Biquaternion.
1910 Encycl. Brit. I. 614/2 Clifford's biquaternions are quantities ξq + ηr, where q, r are quaternions, and ξ, η are symbols (commutative with quaternions) obeying the laws ξ2 = ξ, η2 = η, ξη = ηξ = 0.
This entry has not yet been fully updated (first published 1933; most recently modified version published online June 2018).
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n.1852