Future development. - Matrix new package blog

My goal is to be able to implement basic macroeconomic models on webpages. I discuss some ideas that I might implement in the new Matrix class in the future, depending on their usefulness and the time they might take. Feel free to give some suggestions if you feel they should be part of a matrix class.

I feel this matrix class is an improvement from the previous one, but it still lacks the robustness I need. Moreover, there are still some room for performance improvements and new functions. Here are below the ideas I have to improve this matrix class :

1- Reoptimise code by using the convention that "zero" is not a stored in the vectors and thus, replace for by foreach in most of the routines.

2- Introduce a general Gauss-Seidel algorithm that is more numerically stable than "classic" matrix inversion. This will probably yield new functions such diag (the diagonal of a matrix), upper_tri (upper triangle matrix), and lower_tri (lower triangle matrix) for matrix decomposition.

3- Introduce a method to find eigenvalues (and eigenvectors).

4- Some basic functions such as the trace of a matrix and whatever else that cross my mind which does not take 2000 lines of code.

More generally, I intend to work on :
5- Matrix representation of quadratic approximation of a system of equations and Quadratic regulators.
6- Automatised numerical estimation of the previous point based on a set of "code like" set of equations (if necessary).