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 …

6. Unit quaternions Let Q= (,) and P= (Po, p) be quaternions, where qo, Po E R are the scalar parts of Q and P, q, p are the vector parts. (a) Show that the set of unit quaternions satisfies …

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 …

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 …

Question: Find all the subgroups of the quaternion group, Q8. Which subgroups are normal? What are all the factor groups of Q8 up to isomorphism?

Since you are in the happy position of working with a group of small order, I think you would be well served by writing out the elements of the group, and the product of each pair of elements …

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 …

Quaternion , DCM [Direction Cosine Matrix] , Euler Angles and Rotation Matrix Differences and when to use ? All of the above components can represent rotation , so when to use each of …

You can integrate these by treating the angular velocity vector as a pure quaternion, and using quaternion exponentiation to integrate the velocity over interval $\mathrm {d}t$.

I am looking for books or papers which tell me something about representation theory of finite groups over $\\mathbb{Q}$ (or finite extensions thereof which are not splitting fields of the …