A note on simultaneously diagonalizable matrices
Abraham Berman, Robert J. Plemmons · Mathematical Inequalities & Applications · 1998
Consider the functional f (U) = n i=1 max j {(U T M j U) ii } over orthogonal matrices U , where the collection of n -byn symmetric matrices M j are pairwise commutative, and thus simultaneously diagonalizable. Selecting an orthogonal matrix U which maximizes f (U) has applications in adaptive optics. A proof is given here that any orthogonal matrix Q which simultaneously diagonalizes the M j maximizes the function f .