Timeline for Trace and exterior product
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2019 at 15:55 | answer | added | Bugs Bunny | timeline score: 1 | |
| Aug 22, 2019 at 10:38 | comment | added | Per Alexandersson | @DCM Yes, think it should be something like that, but the expressions I manage to come up with are not symmetric in the eigenvalues, which is absurd. | |
| Aug 22, 2019 at 10:22 | comment | added | DCM | If you know the eigenvalues of the $\wedge^nV$ endomorphism, isn't your trace just going to be the sum of some subset of these? Have you tried doing all the calculations explicitly for your $n=2$ example? Is the difficulty more 'passing to the exterior power' or `passing to an invariant subspace'? | |
| Aug 21, 2019 at 21:10 | comment | added | Per Alexandersson | @AliTaghavi I have not thought about that... | |
| S Aug 21, 2019 at 20:59 | history | suggested | Ali Taghavi |
I add the tag "trace'
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| Aug 21, 2019 at 20:57 | review | Suggested edits | |||
| S Aug 21, 2019 at 20:59 | |||||
| Aug 21, 2019 at 20:56 | comment | added | Ali Taghavi | Is there an interesting NONLINEAR analogy for the spaces you are considering? | |
| Aug 21, 2019 at 20:54 | comment | added | Ali Taghavi | is it true (and obvious) that every every linear symplectomorphism of $\mathbb{R}^{2n}$ preserve $W$? | |
| Aug 21, 2019 at 20:52 | comment | added | Ali Taghavi | Thanks for your edit and giving an example clearing the definition. | |
| Aug 21, 2019 at 20:43 | history | edited | Per Alexandersson | CC BY-SA 4.0 |
added example
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| Aug 21, 2019 at 20:41 | comment | added | Per Alexandersson | @AliTaghavi By convention, there is an order of the indices - increasing. Note that if you know the e-indices, then the f-indices are known as well. The subset of [n] that index the e-part can be chosen in 2^n ways. | |
| Aug 21, 2019 at 20:37 | comment | added | Ali Taghavi | I have difficulty to understand the definition of $W$ since you wrote it has $2^n$ dimension let us consider $n=2$ it is more convenient to put an order on variables $x_1<x_2<y_1<y_2$ so I think you mean a base for $W$ is $x_1 \wedge y_2, x-2\wedge y_1 $ so it is 2 dimensional not 4 dimensional space. what is my error? | |
| Aug 21, 2019 at 20:33 | history | edited | Per Alexandersson | CC BY-SA 4.0 |
added 28 characters in body
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| S Aug 21, 2019 at 20:31 | history | suggested | Ali Taghavi | CC BY-SA 4.0 |
I fix the notation because the previous one could be confused with space of polynomials in 2n variables.
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| Aug 21, 2019 at 20:22 | review | Suggested edits | |||
| S Aug 21, 2019 at 20:31 | |||||
| Aug 21, 2019 at 19:43 | history | asked | Per Alexandersson | CC BY-SA 4.0 |