Here P A j denotes the orthogonal projection on the space spanned by the standard unit vectors corresponding to the elements of A j , so that the matrix of P A j T P A j is obtained from the matrix of T by replacing all rows and columns that don't correspond to the indices in A j by 0. The matrix norm ‖ ‖ ⋅ ⋅ ‖ ‖ is the spectral norm, i.e. the operator norm with respect to the Euclidean norm on C n .