Complex numbers and hamilton quaternions generate [tex]M_{2}(C)[/tex]

[antonio85]

How can $$M_{2}(\mathbb{C})$$ be written as a combination of elements of $$\mathbb{C}$$ and elements of $$\mathbb{H}$$?

 

[Simon_Tyler]

This is a basic result needed in the classification of real Clifford algebras. Se, eg, http://arxiv.org/abs/hep-th/0506011

Basically use the http://en.wikipedia.org/wiki/Quaternions#Matrix_representations" the quaternion algebra.