Matrix dimensions

I am on a side trip to make something similar to Matlab with openGL in a way that I can visualize and represent the various dimensions of a problem in 3 space. Things like eigenvalues, determinants, and NULL space, solution space and attractors or pointing indicators that show characteristics of a matrix solution that might give some insight into making a solver that is consistent and extensible to all problem sets. Dimensionality, logic and arithmetic or calculus are obvious elements that have to be considered and I don't know where I am going with all this, but I suppose I will know when I get there.

I would like to have a way to relate to the existing science, but it becomes more cumbersome to do as time passes. I am tempted to see it as something stone age and I shouldn't do that, but some of the methods are 10^100 times more convoluted and random. That is not an exaggeration for effect. If you look at plant life, you will see that for a specific needed chemical, the energy use is measured in lumps of ATP (Adenosine Tri-Phosphate). In the lab it might be days, thousands of dollars, and mixed results to create a simple Amino Acid sequence. In life the bond with the phosphate group provides the intermediary for almost every process in the cell. It is the coin of life. Consider what effort would have to be employed to make or break a specific bond in a specific molecule of a system without disrupting or changing any other part of the system. I would bet that no lab could actually achieve that without just stealing the process from life itself.