I was recently told about a theorem in linear algebra, involving the eigenvalues of a matrix over the complex numbers. Apparently given a matrix, one can find open sets in the complex plane (or real line, given a symmetric matrix) such that if there's a set of exactly k of them that intersect (really ?? on the condition here, it might be nonempty pairwise intersections) then that subset of the complex plane contains exactly k eigenvalues.

I was told the name of this theorem was something like Gershwin's Theorem. That brings up no relevant info.

I would be grateful if anyone could tell me the name of this theorem, or link me to a wiki/Mathworld reference page.

## What Linear Algebra Theorem Is This?

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### What Linear Algebra Theorem Is This?

SargeZT wrote:Oh dear no, I love penguins. They're my favorite animal ever besides cows.

The reason I would kill penguins would be, no one ever, ever fucking kills penguins.

### Re: What Linear Algebra Theorem Is This?

You mean the Gershgorin Circle Theorem.

http://mathworld.wolfram.com/Gershgorin ... eorem.html

http://mathworld.wolfram.com/Gershgorin ... eorem.html

### Re: What Linear Algebra Theorem Is This?

Thank you so much!

SargeZT wrote:Oh dear no, I love penguins. They're my favorite animal ever besides cows.

The reason I would kill penguins would be, no one ever, ever fucking kills penguins.

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