Timeline for Hodge duality and the determinant of the product of two matrices
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 26, 2016 at 7:08 | history | edited | j.c. | CC BY-SA 3.0 |
fix sign error
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| Feb 23, 2016 at 23:48 | comment | added | darij grinberg | I'd say that the Proposition is a consequence of the Cauchy-Binet formula, the Laplace expansion along the first $n-k$ columns of $M$, and the result (classical?) that a minor of an invertible matrix equals the complementary minor of its inverse (here applied to the matrix with columns $a_1, \ldots, a_k, \widetilde{a}_{k+1}, \ldots, \widetilde{a}_n$, whose inverse is its own transpose). But your proof appears to be a lot simpler... | |
| Feb 23, 2016 at 23:45 | comment | added | darij grinberg | Oh, I've just reread the proposition, and it does make sense now. | |
| Feb 23, 2016 at 23:04 | comment | added | j.c. | @darijgrinberg I see that the $\tilde{a}$'s are not unique, but I think that it doesn't matter (though I should have written "positively oriented orthonormal basis" when introducing them). I am probably missing the thrust of your comment. | |
| Feb 23, 2016 at 22:57 | comment | added | darij grinberg | Isn't your $M $ underdefined? | |
| Feb 23, 2016 at 21:55 | comment | added | Fan Zheng | WLOG suppose $a_i$ are coordinate vectors. Then the result reduces to a trivial computation. | |
| Feb 23, 2016 at 21:16 | history | asked | j.c. | CC BY-SA 3.0 |