Multiplicative relative perturbation bounds of eigenvalues for diagonalizable matrices

Abstract

In this paper, we present the general bounds of multiplicative relative perturbation for diagonalizable matrices, which are the improvement of recent results. The bounds gained here are sharper than those in related literatures. In addition, we obtain the multiplicative relative bounds for normal matrices, which are discussed first.

Keywords:

• multiplicative relative perturbation
• eigenvalues
• diagonalizable matrices
• 2-norm
• F-norm

2000 AMS Subject Classifications :

• 65F10
• 65F15
• 65F35