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 $\ddot{I}{ƒ}_1(A)\ge \cdots \ge \ddot{I}{ƒ}_n(A)>0$. The condition number $\hat{I}º(A):=\ddot{I}{ƒ}_1(A)/\ddot{I}{ƒ}_n(A)=\Vert A\Vert \cdot \Vert A{\Vert }^{-1}$ is a k…