The Euclidean Distance Degree of Orthogonally Invariant Matrix Varieties
  We show that the Euclidean distance degree of a real orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances. 
Dmitriy Drusvyatskiy, Hon-Leung Lee, Giorgio Ottaviani, Rekha R.   Thomas
math.OC