# quaternion

**quaternion**kwətûr´nēən [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

*i*

^{2}=−1. The rules for operating with complex numbers are simply those of operating with the polynomial

*a*+

*bx*except that

*i*

^{2}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

*i*

^{2}=

*j*

^{2}=

*k*

^{2}=

*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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