This paper presents a remarkable formula for spectral distance of a given block normal matrix GD0 = A B C D0 ! to set of block normal matrix GD (as same as GD0 except block D which is replaced by block D0), in which A 2 Cnn is invertible, B 2 Cnm;C 2 Cmn and D 2 Cmm with RankfGDg < n + m 1 and given eigenvalues of matrix M = D CA1B as z1; z2; : : : ; zm where jz1j jz2j jzm1j jzmj. Finally, an explicit formula is proven for spectral distance GD and GD0 which is expressed by the two last eigenvalues ofM.
