ERRATA
1) I forgot to actually put the references in place of their placeholders!
References:
A)"Matrix Analysis & Applied Linear Algebra" by Carl D. Meyer, published by SIAM 2000 (1st Ed.)
B) C) & D) are the previous three papers I wrote, the links to which can be found here(bottom of CV page)
For the three previous papers, obviously all references used in those papers have influenced this current paper.
2)It's going to be awhile before I get the scanned images up. Until then, the two sources I used for visualization tech can be found at http://www.flashandmath.com/mathlets/calc/fungraph/ and also http://www.flashandmath.com/mathlets/calc/param2d/
It's fun to play around with, anyway..
edit 12/31/16: I haven't forgotten about this. I don't have a scanner (or printer, to be honest) at home, so I do all of my scanning up at OSU. I'll put the scanned images/figures up sooner than later, promise.
3) The "Theory" part of "Geometric Lens Theory" may be a misnomer.. I'm not 100% sure if I should be calling it "GLTheory", "GLConjectures", "GLMethodology", or what. I'm looking at this subject as a way to solve different types of problems (with the admission that Zong's "The Cube...." is an inspiration in format, if not content). In that sense, my current feeling (8/12/2016) is that "Methodology" is more appropriate than "Theory".
4)In discussing "topologically equivalent spheres" in the sphere packing hypothesis made in this paper's conclusion, I mean to imply the topology is a metric/differentiable topology, not just a general topology where the metric doesn't matter. The main point being that Ci and As (and their 3-space analogues) are point-wise equivalent in a differential geometric sense (shown in my 2nd paper) as well as having topological equivalence (shown in 1st paper). The argument about non-intersection for all non-pole points that I referred to from the 2nd paper isn't actually explicitly shown, The measurements on distance from origins both planar and derived are shown in the 2nd paper. The application to sphere packing is via implication from those measurements, the concession being that there might be a better chance of achieving a "hybrid packing" by using more elliptic forms of the aster/hyperbolic octahedron (or astroidal ellipsoids, as wolfram calls them)
5) I'd like to state that I have serious apprehensions about A^(-1) both in terms of its calculation AND in regards to it being the best choice for "ubiquitous use" in gL(*)..methodology or whatever we're calling it. But my apprehension is MOSTLY in the calculations department. Just putting it out there.
(Addendum to 5) on 3/30/17:
A^(-1) should be (1/[cos(*)+sin(*)] times the adjugate of A. In the paper, not all entries of the adjugate (specifically the second row entries) had a denominator of [cos(*)+sin(*)]. Essentially;
A^(-1)= adj(A)/det(A). That was my big mistake, and now all apprehensions of calculations for A^(-1) are resolved.)