![]() ![]() On the following day, Hamilton wrote a letter to his friend and fellow mathematician, John T. ![]() Although the carving has since faded away, there has been an annual pilgrimage since 1989 called the Hamilton Walk for scientists and mathematicians who walk from Dunsink Observatory to the Royal Canal bridge in remembrance of Hamilton's discovery. Into the stone of Brougham Bridge as he paused on it. Quaternions are generally represented in the formĪ + b i + c j + d k, Multiplication of quaternions is noncommutative. 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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