The extension of Weyl-type relative perturbation bounds

Relative perturbation theory for eigenvalues of Hermitian positive definite matrices has been well-studied, and the major results were later derived analogously for Hermitian non-singular matrices. In this dissertation we extend several relative perturbation results to Hermitian matrices that are potentially singular, and also develop a general class of relative bounds for Hermitian matrices. As a result, corresponding relative bounds for singular values of rank-deficient $m\times n$ matrices are also obtained using related Jordan-Wielandt matrices. We also discuss a comparison between the main relative bound derived and the Weyl's absolute perturbation bound in terms of their sharpness and derivation in practice.