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Is there an elegant proof of Sylvester's law of inertia available online anywhere? It was set as an exercise in my textbook and I have proved it some time ago but now for the exams I want to know a more succinct proof in case it crops up. Thanks.

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Can you elaborate on the solution you found? If it is in fact too long perhaps we can help you trim it. Most proofs I've seen online seemed reasonably simple and short, so it's not easy to see what else you are looking for. – rschwieb May 22 '12 at 11:17

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