Quaternion

In mathematics, the quaternions are a non-commutative extension of the complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. At first, the quaternions were regarded as pathological, because they disobeyed the commutative law ab = ba. Although they have been superseded in most applications by vectors, they still find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations.

Related Topics:
Mathematics - Non-commutative - Complex number - Irish - Mathematician - Sir William Rowan Hamilton - 1843 - Mechanics - Pathological - Vector - Three-dimensional rotations

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In modern language, the quaternions form a 4-dimensional normed division algebra over the real numbers. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by mathbb H.

Related Topics:
Normed division algebra - Real number - Blackboard bold

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