![]() Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. In mathematics, the quaternion number system extends the complex numbers. (If the image is opened in the Wikipedia commons by clicking twice on it, cycles can be highlighted by hovering over or clicking on them.) Top row shows the post-multiplier.)Ĭayley Q8 graph showing the six cycles of multiplication by i, j and k. Note: This is a multiplication table, not a Cayley table, because inverses do not appear in the row or column headings. For other uses, see Quaternion (disambiguation). This article is about quaternions in mathematics.
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