A couple of observations:

1. You should probably go ahead and implement at least LU decomposition, QR factorization, and maybe some eigenvalue/eigenvector stuff if you want to claim "advanced".

2. You should use the recursive definition of the determinant in the >3x3 matrix case.

3. You should consider adding some vector methods of the form: ax+by (for scalar a & b, and vector x & y). This can be useful for doing linear interpolation and whatnot.

4. You should add cross products/outer products for vectors.

5. You should have a mechanism for generating a Gaussian or normal distribution, or at least supply some standard mappings from your (presumably uniform) random function to something more useful (Gaussian, Possoin, Weibull, whatever).

6. An FFT would be nice. :)

7. Quaternions would also be handy for graphics folks, or motion folks.

8. Complex number support would be cool.

9. Support for optimization, like integer programming, linear programming, or even least-squares or whatever would be nice.

~

Again, great work--I look forward to seeing how this project evolves!