At Ray Koopman's suggestion, I am posting this question concerning whether the following two 12x12 matrices can be "t-tested" to see if they differ significantly. (If this post does not appear in a fixed- font such as Courier, copy/paste the two matrices into a plain text file.)
construct the 66 "n choose 2" pairs ((sl(i),in(i)),(sl(j),in(j))) such that i < j.
Use each of these 66 pairs to determine a unique hyperboloid H(i,j) of one sheet, and rotate each H(i,j) so as to obtain its canonical equation (no cross-terms). For example, using the slope and intercept pairs from rows 3 and 7, generate the equation of H(3,7) with these co- efficients for x^2, y^2, and x^2 respectively:
For ease of reference, denote each of these 66 H's by H(2,i,j) and denote each of the 66 original H's obtained in Steps 1-3 by H(1,i,j).
Compute the distance between any two hyperboloids H(1,u,v) and H(2,g,h) as follows:
"Each hyperb has one negative and two positive coeffs. Say that gives a, a, a and b, b, b. For each i = 1, 3 find the larger of a[i]/b[i], b[i]/a[i]. Add up those three ratios. Identical hyperbs produce a norm of 3. Of course it would be trivial to use some different norm."
(Bob Lewis (Fordham) came up with this norm; as you can see, he's perfectly willing to change it):
Find all pairs of hyperboloids H(1,u,v) and H(2,g,h) for which:
i) the distance between H(1,u,v) and H(2,g,h) is less than 3.1 (according to Bob's norm);
ii) u,g differ by no more than 1 and v,h differ by no more than 1;
iii) if u <> g then v = h, and vice-versa.
Initialize a 12 x 12 matrix "M13" to 0 in each cell, and for each pair of H's found in Step 5, add 1 to cells (u,v) and (g,h) of M13.