Matrix Groups: Part 2

This covers roughly pages 4 to 7 of my notes. Here we study the complex matrices represented as real matrices and quaternionic matrices represented as complex matrices. These natural homomorphisms allow us to reduce everything to a problem of sufficiently large real matrices. Conversely, for a set of real matrices which satisfies the right conditions with respect to the complex or quaternionic structure we can trade the real problem for a corresponding complex or quaternionic problem.