Several years ago I was writing a Machine Learning paper that required me to do rotations in an arbitrary number of dimensions. As such I had an entire section of the paper devoted to explaining how that was done before moving on to the actual algorithm. Here I extracted the portion where I explain N-dimensional rotations, basically rotations in 4-dimensional space or higher, and created its own PDF out of it. I hope this will be of use to some of you to help explain the process. Its a bit math-heavy but I am, as always, happy to answer any questions.