Search results
A quaternion of the form a + 0 i + 0 j + 0 k, where a is a real number, is called scalar, and a quaternion of the form 0 + b i + c j + d k, where b, c, and d are real numbers, and at least one of b, c, or d is nonzero, is called a vector quaternion.
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.
The quaternion is implemented as Quaternion[a, b, c, d] in the Wolfram Language package Quaternions` where however , , , and must be explicit real numbers. Note also that NonCommutativeMultiply (i.e., ** ) must be used for multiplication of these objects rather than usual multiplication (i.e., * ).
The 19th century Irish mathematician and physicist William Rowan Hamilton was fascinated by the role of C in two-dimensional geometry. For years, he tried to invent an algebra of “triplets” to play the same role in three dimenions:
quaternion is a 4-tuple, which is a more concise representation than a rotation matrix. Its geo- metric meaning is also more obvious as the rotation axis and angle can be trivially recovered.
• To present better ways to visualize quaternions, and the effect of quaternion multiplication on points and vectors in 3-dimensions. • To develop simple, intuitive proofs of the sandwiching formulas for rotation
Visualising Quaternions, Converting to and from Euler Angles, Explanation of Quaternions.
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.
Mar 13, 2022 · The quaternions were invented by Sir William Rowan Hamilton about 1850. Hamilton was perhaps the first to note that complex numbers could be thought of as a way to multiply points in the plane. He then had the idea of trying to find a way to multiply points in R3 so that the field axioms would be satisfied.
Jun 7, 2020 · A hypercomplex number, geometrically realizable in four-dimensional space. The system of quaternions was put forward in 1843 by W.R. Hamilton (1805–1865). Quaternions were historically the first example of a hypercomplex system, arising from attempts to find a generalization of complex numbers.
