[catnaroek]

Presumably your target audience cares about the application of PCA, rather than the mathematical technique for its own sake. Thus, you need to answer the question “What does it do for me?” before the question “How does it work?” I believe that the answers to these two questions are, respectively, the geometric interpretation of a PCA, and the algorithm for computing a SVD decomposition. But I could be wrong! If you think I'm wrong, please tell me how.