Timeline for A metric for Grassmannians
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| S Mar 31, 2022 at 5:35 | history | suggested | Alp Uzman | CC BY-SA 4.0 |
Corrected paper title; added doi, changed a tag
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| Mar 31, 2022 at 4:39 | review | Suggested edits | |||
| S Mar 31, 2022 at 5:35 | |||||
| Jul 14, 2015 at 20:51 | comment | added | Jairo Bochi | "Natural" metrics on the Grassmannian should be invariant under isometries of the undelying Euclidian space. Actually there are many such metrics, and this nice paper gives a general method for constructing them: Qiu, Zhang, Li, "Unitarily invariant metrics on the grassmann space". SIAM J. Matrix. Anal. Appl. vol 27, no 2, 507-531. | |
| Mar 19, 2015 at 1:02 | comment | added | Daniele Zuddas | what about the angle between $W_1$ and $W_2$? It seems to be a distance taking values in $[0, \pi/2]$ | |
| Mar 18, 2015 at 22:08 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
removed tag 'metric' created by previous edit; fixed the question statement; do not know precisely what article the question refers to, so did not fix it
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| Mar 18, 2015 at 22:08 | answer | added | Jairo Bochi | timeline score: 6 | |
| S Mar 18, 2015 at 21:24 | history | suggested | Jairo Bochi | CC BY-SA 3.0 |
Added tags
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| Mar 18, 2015 at 21:07 | review | Suggested edits | |||
| S Mar 18, 2015 at 21:24 | |||||
| Mar 18, 2015 at 21:04 | comment | added | Jairo Bochi | @RyanBudney The Riemannian metric from your second suggestion is explicitly described in this 1967 paper pnas.org/content/57/3/589.full.pdf+html which also describes geodesics and other interesting stuff. | |
| Dec 7, 2010 at 22:12 | vote | accept | CommunityBot | ||
| Dec 6, 2010 at 13:33 | answer | added | Ian Morris | timeline score: 23 | |
| Dec 4, 2010 at 13:35 | vote | accept | CommunityBot | ||
| Dec 7, 2010 at 22:12 | |||||
| Dec 3, 2010 at 4:01 | answer | added | R W | timeline score: 11 | |
| Dec 3, 2010 at 0:53 | comment | added | Ryan Budney | Another way is to view the Grassmannian as a homogeneous space, i.e. as a quotient of a Lie group by a compact subgroup. Homogeneous spaces inherit metrics as quotient spaces, since compact Lie groups have invariant metrics. | |
| Dec 3, 2010 at 0:51 | comment | added | Ryan Budney | Given two $k$-dimensional vector subspaces $W_1$, $W_2$ of a common vector space $V$, let $d(W_1,W_2)$ be the Hausdorff distance between $W_1 \cap S$ and $W_2 \cap S$ where $S$ is the unit sphere in your vector space -- assuming your vector space has an inner product. See: en.wikipedia.org/wiki/Hausdorff_distance | |
| Dec 3, 2010 at 0:38 | history | asked | user11178 | CC BY-SA 2.5 |