Quaternions: Difference between revisions
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imported>Jitse Niesen m (spelling and grammar) |
imported>Fredrik Johansson (The "Introduction" heading isn't necessary; introductory paragraph should go above table of contents. Downcasing.) |
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'''Quaternions''' are a [[Commutativity|non-commutative]] extension of the [[Complex number|complex numbers]]. They were first described by Sir William Rowan Hamilton in 1843. He famously inscribed their defining equation on Broom Bridge in Dublin when walking with his wife on 16 October 1843. They have many possible applications, including in computer graphics, but have during their history proved comparatively unpopular with [[vector]]s being preferred instead. | '''Quaternions''' are a [[Commutativity|non-commutative]] extension of the [[Complex number|complex numbers]]. They were first described by Sir William Rowan Hamilton in 1843. He famously inscribed their defining equation on Broom Bridge in Dublin when walking with his wife on 16 October 1843. They have many possible applications, including in computer graphics, but have during their history proved comparatively unpopular with [[vector]]s being preferred instead. | ||
== Definition & | == Definition & basic operations == | ||
The | The quaternions, <math>\mathbb{H}</math>, are a four-dimensional normed division algebra over the [[Real number|real numbers]].<br/><br/> | ||
:<math>\mathbb{H}=\left\lbrace a+\mathit{i}b+\mathit{j}c+\mathit{k}d|a,b,c,d\in\mathbb{R}\right\rbrace</math><br/> | :<math>\mathbb{H}=\left\lbrace a+\mathit{i}b+\mathit{j}c+\mathit{k}d|a,b,c,d\in\mathbb{R}\right\rbrace</math><br/> | ||
:<math>\mathit{i}^2=\mathit{j}^2=\mathit{k}^2=\mathit{ijk}=-1</math> | :<math>\mathit{i}^2=\mathit{j}^2=\mathit{k}^2=\mathit{ijk}=-1</math> | ||
Revision as of 09:14, 22 April 2007
Quaternions are a non-commutative extension of the complex numbers. They were first described by Sir William Rowan Hamilton in 1843. He famously inscribed their defining equation on Broom Bridge in Dublin when walking with his wife on 16 October 1843. They have many possible applications, including in computer graphics, but have during their history proved comparatively unpopular with vectors being preferred instead.
Definition & basic operations
The quaternions, , are a four-dimensional normed division algebra over the real numbers.
