### Author Topic: Problem 1  (Read 16458 times)

#### Fanxun Zeng

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##### Re: Problem 1
« Reply #15 on: December 20, 2012, 02:12:38 AM »
In addition to Part c solution I posted above, here is Problem 1 Part e Bonus solution to prove eigenvalues are simple.

#### Victor Ivrii

In each of three zones number of negative eigenvalues stays the same as they can cross to positives only on the borders. So in fact one can go along line $\alpha=\beta$ which intersects all of them. Then things are slightly simpler to analyze.