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The quaternions are a four-dimensional extension of the two-dimensional complex numbers. They form a non-associative normed division algebra over the real numbers.

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  • Quaternion
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  • The quaternions are a four-dimensional extension of the two-dimensional complex numbers. They form a non-associative normed division algebra over the real numbers.
  • 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 Although they have been superseded in most applications by vectors, they still find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional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.
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  • The quaternions are a four-dimensional extension of the two-dimensional complex numbers. They form a non-associative normed division algebra over the real numbers.
  • 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 Although they have been superseded in most applications by vectors, they still find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional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. 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 .
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