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@rasher Well, not entirely. TraditionalForm evaluates (1/2^24)^x to 16777216^-x whereas HoldForm doesn't use a C notation but outputs Binomial[10000000-1, x]. I wonder if there's some kind of merge of the two? :)
I've tried other matrices that have the same properties, i.e. 1) each column sums to either 1 or 0 and 2) reasonably sparse. For instance, pastebin.com/LczndfTL Same as the one I first posted, it's taking forever.