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The quaternion is called the vector part (sometimes imaginary part) of q, and a is the scalar part (sometimes real part) of q. A quaternion that equals its real part (that is, its vector part is zero) is called a scalar or real quaternion, and is identified with the corresponding real number. That is, the real numbers are embedded in the ...
Oct 10, 2021 · A quaternion of the form xi + yj + zk ↔ (0, x, y, z) is called a pure quaternion or an imaginary quaternion. For a quaternion r = a + bi + cj + dk, we call the real quaternion a the scalar part or real part of r, and we call the quaternion xi + yj + zk the vector part or the imaginary part of r.
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., * ).
Visualising Quaternions, Converting to and from Euler Angles, Explanation of Quaternions.
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:
A scalar (also a scalar quaternion or a real quaternion)) is a quaternion with vector part equal to 0. Example 1.3. 2+3^{ 1|^+2k^ is a quaternion, 3^{ 1^|+2^k is a pure quaternion and 7 is a scalar.
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 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.
Quaternion algebra is one possible way to represent 3 dimensional orientation, or other rotational quantity, associated with a solid 3D object. If you are not familiar with this subject you may like to look at the following pages first:
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.
