Additional file 2 of On the rank-distance median of 3 permutations

Example of numerical unstability of “triple-null” formula in the Implementation section. This Additional file, in text format suitable to be read by Octave or MATLAB, contains three 100×100 matrices A,B, and C for which the triple-null formula does not work, and the alternative single-null formula for the intersection im ( A − B ) ∩ im ( C − B ) $\text {im}(A-B) \cap \text {im}(C-B)$ was used. The file can be checked in Octave as follows: Save it as triple.mat, Call Octave, and then type in its prompt: > load(“triple.mat”) > meet = null([(null(A’-B’))’;(null(C’-B’))’]); > size(meet) ans = 100 0 > meet = orth((A-B)*null([A-B C-B])(1:100,:)); > size(meet) ans = 100 2 This shows that, while the first formula produced a zero-dimensional subspace, the second one actually produced a 2-dimensional subspace. (MAT 222 kb)