re-Learning the basics

Version 3.Ok, now I admit I have gone overboard with the layout of this, so I will quit after 1 more. I have the concept wrong associatively and need to fix it. It is conceptually wrong ( but very artistic ) so I will fix it tomorrow and add the code that solves the Matrix, the vector cross products done in 'c' || Python + openGL, reduction, substitutions and 3D perspective of the intersections of planes ( with normals and different textures for each plane ).

This top one is probably better as it highlights the association of origins of the values and how this might relate to solutions. It uses '\bmatrix' to enclose and '\color{color}'. So the equations that go with this are:
[ 2x  - y       =  0] ,
[  -x+2y-3z = -1],
[      -  y+4z =  4].
So they could be viewed as 3space vectors.

I use matrix calculations all the time for openGL and other situations, and I know how to use them, but do I understand what it means? I guess I have answered that question for myself. By going back over basics again and again, at some point something clicks and you can say, Aha! that is the relationship and if I were completely skilled at AI, I could code that into a neural net of some fashion. I am not at that level yet.

I just completed nearly 110 hours of lectures on subjects ranging from astrophysics of neutron stars, thermodynamics, angular momentum, programming algorithms, hacking, assembly, calculus, trigonometry, Fourier, topology and numerous other subjects from Academic Earth, and other places. I am WAY smarter than I was a week ago and also see that I have plenty of room to improve.

Somehow today, the calculus, vectors, matrix math, and my experience connected and now I have gained from that association too.

I really don't like Lisp as a language, but some of the concepts are very interesting and I may try to lay them out in a 'C' structure for testing. Some new things I learned about PHP and HTML and TCP protocols are going to be a great advantage if I can apply them. My personal Wiki is getting very cluttered and I may have to make some design changes ( in Zim ) that incorporate HASH or SQL or trees or associative context switching to make it easier to use.

I used NRZ and NRZI and numerous other technologies of compression over the years and I guess I always focused on how do I use them and how do I rate them, but never really understood the underlying things like "entropy of information". I still don't, but I am beginning to see how this relates to real entropy as defined by thermodynamics.

To be consistent, I am including the LaTex in the post, but in the future I will include it in the image mouse over to reduce clutter.

\mathcal{A}=\begin{vmatrix}
+2 & -1 &  0\! \\
-1 &  +2 & -3 \\
0\! & -1 &  +4
\end{vmatrix}
=
\begin{vmatrix}
x \\
y \\
z
\end{vmatrix}
\begin{vmatrix}
0\! \\
-1 \\
+4
\end{vmatrix}