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 …

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 $ …

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 …

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 …

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 …

数学背景 四元数变换 (Quaternion Transforms) 连接两个四元数 矩阵和四元数相互转换 球面线性插值 从一个向量旋转到另一个向量)Rotation from One Vector to Another 1 数学背景 …

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 …

Aug 5, 2015 · 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 …

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 …

Firstly, besides the $ijk=-1$, etc definition, what exactly is a quaternion? What is their geometric representation and how does this differ from the representation of complex numbers on the …