Sebastiaan's Subspace

My journal about mathematics and other interests

Category: Linear Algebra

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.

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Continuity of polynomial roots

It was recently brought up how to show that the n 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.

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