I can't write comments, but you want some constraint on X like columns of X have norm 1 and are orthogonal to each other? This is stronger than the constraint suggested by loup blanc. X could be unique only up to permutations of its columns.

I don't have enough reputation to comment, but I wonder how meaningful it is to talk about the centre of mathematics. An earlier question about this concept did not go over so well: mathoverflow.net/questions/131800