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The quaternion number system extends the complex numbers.
Quaternions were first described by Irish mathematician
William Rowan Hamilton in 1843[1][2]
and applied to mechanics in three-dimensional space.

Hamilton defined a quaternion as the quotient of two directed lines
in a three-dimensional space,[3] or equivalently,
as the quotient of two vectors.[4]
Multiplication of quaternions is noncommutative.

In modern mathematical language,
quaternions form a four-dimensional associative normed division algebra
over the real numbers, and therefore also a domain.

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