Timeline for Some calculus in the orthogonal group $O(n)$
Current License: CC BY-SA 3.0
22 events
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| Jan 30, 2015 at 11:54 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 30, 2015 at 11:47 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 30, 2015 at 10:07 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 28, 2015 at 6:00 | comment | added | Ali Taghavi | @CarloBeenakker thank you very much for your very interesting answer. | |
| Jan 28, 2015 at 5:27 | vote | accept | Ali Taghavi | ||
| Jan 27, 2015 at 9:17 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 27, 2015 at 9:17 | comment | added | Carlo Beenakker | deleted "simplistic argument" for the first integral in my answer: the result for $p$ odd is obvious because contributions $\pm g$ to the integral cancel; the result for $p$ even follows without calculation from the fact that only eigenvalues $\pm 1$ of the orthogonal matrix $g$ contribute to the average of the trace (the complex eigenvalues average out to zero); for $n$ odd every $g$ has one such eigenvalue, so the average is one, for $n$ even and ${\rm det}\,g=+1$ there are no such eigenvalues but for ${\rm det}\,g=-1$ there are two, so the average is again one. | |
| Jan 27, 2015 at 9:10 | comment | added | Carlo Beenakker | @WillSawin --- good point, this is not obvious, so I have removed the "simple argument", which was apparently too simple; for the record, it follows after this comment. Thanks for correcting me. | |
| Jan 27, 2015 at 9:09 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 22:59 | comment | added | Will Sawin | Why do the complex eigenvalues average out to 0? | |
| Jan 26, 2015 at 12:57 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 12:26 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 12:10 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 12:01 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 11:44 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 11:37 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 11:26 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 11:20 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 11:09 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 10:56 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 9:53 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jan 26, 2015 at 9:34 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |