BOUNDS FOR THE SMALLEST SINGULAR-VALUE OF A JORDAN BLOCK WITH AN APPLICATION TO EIGENVALUE PERTURBATION

Let J(m, A) be an m X m Jordan block with lambda on its diagonal, and sigma1(m, lambda) be its smallest singular value. As sigma1(m, lambda) = sigma1(m, Absolute value of lambda), denoting delta = Absolute value of lambda, we obtain the following inequalities: [GRAPHICS] As a direct result of the inequalities, a lower bound on the perturbation of eigenvalues in the case of a more general matrix is given.