四元数 (quaternion)可以看作中学时学的复数的扩充，它有三个虚部。 形式如下： ，可以写成 具有如下性质： 设 ， ，则 3.2 共 轭四元数 一个四元数 的共轭 (用 表示)为 一个四元数和它的共轭的积等于 …

The quaternion algebra shows there as a way of disentangling two Alamouti coded signals transmitted by a pair of antennas. The advantages come from the fact that even if the signal from one antenna is …

Oct 19, 2010 · Here is the intuitive interpretation of this. Given a particular rotation axis $\omega$, if you restrict the 4D quaternion space to the 2D plane containing $ (1,0,0,0)$ and $ …

Aug 5, 2015 · The idea of Hamilton was to find some generalization of this formula for three-dimensional rotations. The quaternions can do such a generalization identifying a $3D$ -vector with a pure …

Aug 11, 2014 · One of the quaternion elements is guaranteed to have a magnitude of greater than 0.5 and hence a squared value of 0.25. We can use this to determine the "best" set of parameters to use …

May 27, 2020 · Of course adding two quaternions gives a quaternion, so algebraically this is clear. I don't really think it's clear geometrically, however, and with good reason: this is a very exceptional …

Jun 24, 2022 · I am trying to find a way of converting a quaternion from an arbitrary coordinate system to a fixed coordinate system that is used in my application. I have two different coordinate systems, one …

Feb 3, 2017 · If I combine 2 rotation quaternions by multiplying them, lets say one represents some rotation around x axis and other represents some rotation around some arbitrary axis. The order of …

Do one quaternion multiplication and you rotate the circular component just that far around, and the quaternion axis gives you the rest of the location, and the fourth dimension says how far ahead or …

Apr 13, 2013 · A nice thing is that multiplication of two normalized quaternions again produces a normalized quaternion. Quaternion inversion (or just conjugate for the normalized case) creates the …