Calculate with quaternions in matrix form

Question

I am working on a software implementation of Matrices, Quaternions and Vectors ($\mathbb{R}^3$ and $\mathbb{R}^2$), but I want all of them to use matrices as underlying form.

I already found out that a vector dot product equals $\vec{a}^T \ \vec{b}$, but what about:

• cross products
• hamilton products
• quaternion multiplication?

Can they, too, be represented as matrix operations?

Answer 1

See cross product matrix and the matrix representations of quaternions on Wikipedia.