diagonalize

To convert a square matrix into a diagonal matrix by multiplying it by a second matrix and its inverse.

To design variables such that design problems only bear upon subsets that are loosely coupled to others.

And what we should do, therefore, is to diagonalize the variables—we should find some new design variables such that design problems only bear upon subsets of them that are loosely coupled to others, like the subsystems of ten lights in the example.