Idea – Sort The Matrix Before Doing Calculations?

I wonder. Should there not be a reward or any kind of mathematical gain for doing transformations. Lossless transformations in particular. I think this could be true. 
One kind of transformation I think of is sorting to a index and value matrix of a matrix.

I did this for a random matrix of some size. The idea is that this transformation into a real valued matrix and two sorted matrixes of integers will better, faster or something when doing some calculation.