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 …

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 $ …

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 …

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 …

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 …

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 …

Oct 27, 2022 · A quaternion can be thought of as a scalar plus a 3D vector (also known as real and imaginary parts). The product of a scalar and a 3D vector is the usual scalar multiplication. The …

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 13, 2016 · This is a slightly complicated question but put simply. C is the field over R such that it is of the form (a+bi) where (a,b) are in R. The quaternion is a further extension where numbers are 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 …