Timeline for Doubly-stochastic partial-isometric matrices
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 5, 2020 at 12:08 | history | edited | vidyarthi | CC BY-SA 4.0 | deleted 454 characters in body |
| Jul 31, 2020 at 22:48 | history | edited | vidyarthi | CC BY-SA 4.0 | deleted 19 characters in body |
| Jul 31, 2020 at 22:13 | comment | added | Ruy | Let us continue this discussion in chat. | |
| Jul 31, 2020 at 21:46 | history | edited | vidyarthi | CC BY-SA 4.0 | added 1 character in body |
| Jul 31, 2020 at 21:30 | comment | added | vidyarthi | @Ruy thanks. edited the post. see now | |
| Jul 31, 2020 at 21:29 | history | edited | vidyarthi | CC BY-SA 4.0 | added 478 characters in body |
| Jul 31, 2020 at 19:46 | comment | added | Ruy | Stochastic matrices must have nonnegative entries (which often represent transition probabilities). | |
| Jul 31, 2020 at 19:37 | comment | added | vidyarthi | @Ruy as I said, the discussion in the second discussion applies to unscaled matrices, that is, the row and column sums are same for the matrix. The matrix you gave as an example is definetely doubly stochastic. The row and column sums are all $1$ | |
| Jul 31, 2020 at 17:23 | comment | added | Ruy | I think this is not yet correct. The matrix $ E={1\over30}\pmatrix{ 25& -5& 10 \cr -5& 25& 10 \cr 10& 10& 10} $ is idempotent and has $(1,1,1)$ as a fixed point and yet it is not doubly-stochastic. | |
| Jul 31, 2020 at 13:21 | history | edited | vidyarthi | CC BY-SA 4.0 | added 722 characters in body |
| Jul 31, 2020 at 1:22 | comment | added | Ruy | I think I can prove that your conclusion is corrrect, but the proof is a bit envolving. Will try to write it down soon. | |
| Jul 31, 2020 at 1:03 | comment | added | Ruy | Now I should say that I do not see why 𝑈, 𝐷, and 𝐸 must be scalar multiples of doubly stochastic matrices. | |
| Jul 30, 2020 at 21:33 | comment | added | vidyarthi | @Ruy yes, they need not be. Added the scaling factors | |
| Jul 30, 2020 at 21:22 | history | edited | vidyarthi | CC BY-SA 4.0 | added 67 characters in body |
| Jul 30, 2020 at 21:14 | comment | added | Ruy | I do not see why $U$, $D$, and $E$ must be doubly stochastic. But the guess is certainly very interesting! | |
| Jul 30, 2020 at 21:08 | history | undeleted | vidyarthi | ||
| Jul 30, 2020 at 21:08 | history | edited | vidyarthi | CC BY-SA 4.0 | added 24 characters in body |
| Jul 30, 2020 at 20:33 | history | deleted | vidyarthi | via Vote | |
| Jul 30, 2020 at 20:30 | history | edited | vidyarthi | CC BY-SA 4.0 | added 1 character in body |
| Jul 30, 2020 at 20:17 | history | answered | vidyarthi | CC BY-SA 4.0 |