## Continuity of eigenvalues

As a simple corollary to the result from my previous post I would like to show you how to obtain continuous dependence of the eigenvalues of a matrix on its entries. Specifically, let be the complex vector space of matrices with entries in , endowed with any norm of our… Read moreContinuity of eigenvalues

## Continuity of polynomial roots

It was recently brought up how to show that the roots of a real or complex polynomial depend continuously on the polynomial’s coefficients. Although I have used this proposition numerous times, implicitly and explicitly, I realized that I never saw a proof of it. Perhaps the most obvious approach would… Read moreContinuity of polynomial roots