- an expression of the form a + bi + cj + dk, where a, b, c, and d are real numbers; i2 = j2 = k2 = −1; and ij = −ji = k, jk = −kj = i, and ki = −ik = j.
- a quantity or operator expressed as the sum of a real number and three complex numbers, equivalent to the quotient of two vectors. The field of quaternions is not commutative under multiplication.
Origin of quaternion
Examples from the Web for quaternion
Four soldiers formed a quaternion; four quaternions therefore were sixteen men, who were especially appointed to guard Peter."Granny's Chapters"|Lady Mary Ross
The quaternion was a gathering of four sheets of vellum, each folded once; thus forming sixteen pages.Illuminated Manuscripts in Classical and Mediaeval Times|J. Henry Middleton
These last words are incorrect in fact, for οὐκ ἄνθρωπος does not appear in the first Quaternion, but is reserved for the second.Aristotle|George Grote
His days are thus described: from dawn to the third hour he copied rapidly, filling a (quaternion) each day.The Mediaeval Mind (Volume I of II)|Henry Osborn Taylor
William Hare, the second of our quaternion, was also a native of Ireland, having been born in the neighbourhood of Londonderry.The Court of Cacus|Alexander Leighton