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APM346-2012
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APM346 Math
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Home Assignment 4
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Problem 1
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Topic: Problem 1 (Read 39687 times)
Fanxun Zeng
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Posts: 36
Karma: 11
Re: Problem 1
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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.
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Victor Ivrii
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Re: Problem 1
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Reply #16 on:
December 20, 2012, 02:39:30 AM »
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.
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Toronto Math Forum
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APM346-2012
»
APM346 Math
»
Home Assignment 4
»
Problem 1