Timeline for Doubly-stochastic partial-isometric matrices
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 10, 2020 at 0:58 | vote | accept | Ruy | ||
| Jul 31, 2020 at 2:34 | answer | added | Ruy | timeline score: 0 | |
| Jul 30, 2020 at 21:11 | comment | added | Ruy | @vidyarthi, here are two results from Halmos' "A Hilbert Space Problem Book", which say that the two characterizations are equivalent: (Problem 127) A bounded linear transformation $U$ is a partial isometry if and only if $U^*U$ is a projection, and (Corollary 3) A bounded linear transformation $U$ is a partial isometry if and only if $U = UU^*U$. | |
| Jul 30, 2020 at 21:09 | comment | added | vidyarthi | @ChrisRamsey see my answer now. | |
| Jul 30, 2020 at 20:45 | comment | added | Chris Ramsey | @vidyarthi Any doubly stochastic idempotent will be a partial isometry. The OP gives a description of the idempotents and most are not permutations. | |
| Jul 30, 2020 at 20:40 | comment | added | vidyarthi | @ChrisRamsey But I think the equation in the question describes an isometry. I think the right equation is $(AA^t)^2=AA^t$, right? | |
| Jul 30, 2020 at 20:17 | answer | added | vidyarthi | timeline score: -1 | |
| Jul 30, 2020 at 16:16 | history | edited | Chris Ramsey | Added matrices tag for better visibility. | |
| Jul 29, 2020 at 17:52 | history | asked | Ruy | CC BY-SA 4.0 |