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I have been going over the code, and maybe I am just thick, but do any of the decompositions that require it perform a test for positive definiteness (or semi-definiteness?). I notice there is a TODO in the Cholesky decomposition class about it?
If not, would you want me to write a method in the Matrix class to test for positive definite (PD) and positive semi-definite(PSD) matrices? My proposed implementation would be:
1. Check to see if it is symmetric row diagonally-dominant - if it is then it is PSD, if not....
2. Check whether each principle submatrix has a determinant greater than (PD) or equal to (PSD)
For large matrices this is the most efficient method I am aware of. Anyone have any better ideas?
I have this code currently in the LDL/UDU decompositions that I need for square-root Kalman filtering... Once these classes make it into Iridium, I can push my Kalman filters into Neodym.

In fact, while I reflect on it, is there any reason there are no methods in the Matrix class for:
IsSymmetric()
IsPositiveDefinite()
IsPositiveSemiDefinite()
They are all rather handy when dealing with covariance matrices! I'll create issues in the tracker, and if you want me to address them, just assign them to me. I already have soem reasonably solid code for them in my Kalman Filter classes

There's no reason, it just wasn't done yet. Hence, yes, please implement them. Thanks!

(You may want to consider caching the results using the on-demand computation pattern, and then (only then) use properties instead of methods.)

Some other missing properties that might be interesting to provide: see older forum post. I'll create some feature requests in the tracker for them.