Eigenvalue stability and new perturbation bounds for the extremal eigenvalues of a matrix

Phuc Tran, Van Vu

Let $A$ be a full ranked $n\times n$ matrix, with singular values ${\sigma }_1(A)\ge \cdots \ge {\sigma }_n(A)>0$. The condition number $\kappa (A):={\sigma }_1(A)/{\sigma }_n(A)=\Vert A\Vert \cdot \Vert A{\Vert }^{-1}$ is a key pa…