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 …

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 $ …

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 …

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 …

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. …

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 …

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 …

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 …

Oct 19, 2021 · In the context of using unit quaternions to represent 3D rotations, I'm aware that the inverse is the conjugate. So if I have a unit quaternion Q = {qw, qx, qy, qz} (where qw is …

where log/exp are the quaternion logarithm/exponential. If you can convert between rotation vectors (where the direction is the rotation axis and the magnitude is the angle) and …