quaternion kw?trn??n [key], in mathematics, a type of higher complex number first suggested by Sir William R. Hamilton in 1843. A complex number is a number of the form a+bi when a and b are real numbers and i is the so-called imaginary unit defined by the equation i2=?1. The rules for operating with complex numbers are simply those of operating with the polynomial a+bx except that i2 is replaced by ?1 whenever it occurs. A quaternion, an extension of this concept, is a number of the form a+bi+cj+dk when a, b, c, and d are real numbers and i, j, and k are imaginary units defined by the equations i2=j2=k2=ijk=?1. Quaternions, as well as vectors and tensors (later outgrowths of the concept of quaternions), have many important applications in mechanics.

The Columbia Electronic Encyclopedia, 6th ed. Copyright 2012, Columbia University Press. All rights reserved.

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