Wow!  It finally happened.  I managed to compute a covariance matrix from "real world" data that was singular. The good news is that I found a failure in my row swapping logic for inverting a matrix.  The bad news is that no matter how I rearranged the rows of data, the determinant was always zero.

This just goes to show that singlular matrices may be rare in the "real world", but they do exist.  It also points out that my well thought out unit test wasn't.   The term "failed spectacularly" comes to mind.

This problem goes back to the drawing board for further analysis.