如何形象地理解四元数？ 关于 quaternion 的资料（包括网络教程与书籍）已经看过很多，但大脑内无法形成对 quaternion 的形象理解。 请问是否要对群论、四维赋范… 显示全部 关注者 …

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 …

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 …

2010年10月19日 · 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 …

2015年8月5日 · Every quaternion multiplication does a rotation on two different complex planes. When you multiply by a quaternion, the vector part is the axis of 3D rotation. The part you want …

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 …

2013年4月13日 · A nice thing is that multiplication of two normalized quaternions again produces a normalized quaternion. Quaternion inversion (or just conjugate for the normalized case) …

2022年6月24日 · 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 …

2017年1月16日 · 10 (assume "quaternion" implies unit-magnitude quaternion) The thing to understand is that quaternions are not closed under elementwise-addition like vectors are. The …

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 …