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In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 [1] [2] and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by .
Oct 10, 2021 · A quaternion of the form \(a=a+0i+0j+0k\leftrightarrow (a,0,0,0)\) is called a scalar quaternion or a real quaternion. A quaternion of the form \(xi+yj+zk\leftrightarrow (0,x,y,z)\) is called a pure quaternion or an imaginary quaternion.
Mar 10, 2017 · Quaternions are mathematical operators that are used to rotate and stretch vectors. This article provides an overview to aid in understanding the need for quaternions in applications like space navigation. Accurately locating, shifting, and rotating objects in space can be done in a variety of ways.
The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton.
ions provide ‘the’ way to represent rotations. Why? Unit quaternions allow a clear visualization (see Hanson, 2006) of the space of rotations as the unit sphere S.
Quaternions form an interesting algebra where each object contains 4 scalar variables (sometimes known as Euler Parameters not to be confused with Euler angles), these objects can be added and multiplied as a single unit in a similar way to the usual algebra of numbers.
Jun 27, 2024 · quaternion, in algebra, a generalization of two-dimensional complex numbers to three dimensions. Quaternions and rules for operations on them were invented by Irish mathematician Sir William Rowan Hamilton in 1843. He devised them as a way of describing three-dimensional problems in mechanics.
