Quaternion

The quaternions are a division ring (that is, a ring in which each element has a multiplicative inverse; alternatively, a noncommutative field) which generalize the complex numbers.

Formally, the quaternions are the set , where are any real numbers and the behavior of is "as you would expect," with the properties:

• 
• , and

Note in particular that multiplication of quaternions is not commutative. However, multiplication on certain subsets does behave well: the set act exactly like the complex numbers.

See Also

• Real numbers
• Complex numbers
• Rational numbers
• Integers
• Irrational number
• Transcendental number

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