Nearest southeast submatrix that makes multiple an eigenvalue of the normal northwest submatrix
Juan-Miguel Gracia, Francisco E. Velasco · Operators and Matrices · 2012
Let A,B,C,D be four complex matrices, where D C mm and A C nn is a normal matrix. Let z 0 be an fixed eigenvalue of A . We find the distance (with respect to the 2 -norm) from D to the set of matrices X C mm such that z 0 is a multiple eigenvalue of the matrix A B C X .