Comments on: Sylvester's Law of Inertia and *-Congruence http://www.njohnston.ca/2009/08/sylvesters-law-of-inertia-and-congruence/ A blog of recreational math and quantum information theory Mon, 06 Feb 2012 21:25:22 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Ed http://www.njohnston.ca/2009/08/sylvesters-law-of-inertia-and-congruence/#comment-921 Ed Wed, 20 Apr 2011 03:04:05 +0000 http://www.nathanieljohnston.com/?p=562#comment-921 This is a really good way to generalise Sylvester's intertia law! I'm having trouble with the last part of the proof though. When you say "It follows by a simple entry-wise calculation that..." I can't see why this is (and I just go around in circles with the matrix algebra until my head spins). Isn't there some method of proving directly that *-congruence preserves the spectra up to a scale (or rather it preserves the projection of the spectra onto U(1))? [I can't] This is a really good way to generalise Sylvester’s intertia law!

I’m having trouble with the last part of the proof though. When you say “It follows by a simple entry-wise calculation that…” I can’t see why this is (and I just go around in circles with the matrix algebra until my head spins).

Isn’t there some method of proving directly that *-congruence preserves the spectra up to a scale (or rather it preserves the projection of the spectra onto U(1))? [I can't]

]]> By: Nathaniel http://www.njohnston.ca/2009/08/sylvesters-law-of-inertia-and-congruence/#comment-103 Nathaniel Mon, 18 Jan 2010 15:53:24 +0000 http://www.nathanieljohnston.com/?p=562#comment-103 Awesome! Good luck with prelims :D Awesome! Good luck with prelims :D

]]> By: Nick http://www.njohnston.ca/2009/08/sylvesters-law-of-inertia-and-congruence/#comment-102 Nick Mon, 18 Jan 2010 00:38:39 +0000 http://www.nathanieljohnston.com/?p=562#comment-102 Studying linear algebra for my prelim's here at mac, I google Sylvester's Law of Inertia, and you are result number 2. (next only to wikipedia).. you're teaching me math even though i'm over at mcmaster now :) Studying linear algebra for my prelim’s here at mac, I google Sylvester’s Law of Inertia, and you are result number 2. (next only to wikipedia).. you’re teaching me math even though i’m over at mcmaster now :)

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