Estimation of the Separation of Two Matrices (Ⅱ)

Abstract

In this paper we give a lower bound of the separation $sep_F(A,B)$ of two diagonalizable matrices A and B. The key to finding the lower bound of $sep_F(A,B)$ is to find an upper bound for the condition number of a transformation matrix Q which transforms a diagonalizable matrix A to a diagonal form. The obtained lower bound of $sep_F(A,B)$ involves the eigenvalues of A and B as well as the departures form the normality $\delta_F(A)$ and $\delta_F(B)$.