Timeline for How to draw a random normal matrix?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 6, 2017 at 8:58 | vote | accept | Domin | ||
| Sep 3, 2017 at 19:28 | answer | added | Adrien Hardy | timeline score: 4 | |
| Sep 1, 2017 at 12:58 | comment | added | Domin | @Marcel Yes, I did. It is relatively easy to draw a complex random normal matrix (as CarloBeenakker points out), however I would like the matrix to have only real entries. | |
| Sep 1, 2017 at 6:53 | comment | added | Carlo Beenakker | @Marcel --- please correct me if I'm wrong, but if I decompose $A=UDU^\dagger$ with $U$ orthogonal then $A$ is symmetric; I presume the OP wants real normal matrices that are not symmetric (otherwise the question is trivial) | |
| Sep 1, 2017 at 4:49 | comment | added | Domin | @NateEldredge Yes, I know. The motivation is simply this. Imagine, there is a matrix equality for normal real matrices you would like to prove or disprove. Before you get to work. you might want to try a random series of matrices of some size and computationally check whether the equality holds. I am not after any particular distribution, but definitely it should not be sigular w.r.t. the natural measure inherited from $R^{n\times n}$. In other words, each normal matrix should have a chance of being drawn. | |
| Aug 31, 2017 at 22:57 | comment | added | Marcel | @CarloBeenakker no, the papers I mean interpret "normal" in the sense of the question (although I think the ensembles are indeed Gaussian). Also, to make your $A$ real one just draws random orthogonal matrices, no? | |
| Aug 31, 2017 at 22:00 | comment | added | Igor Rivin | @CarloBeenakker What is the distribution of the coefficients of this? | |
| Aug 31, 2017 at 21:07 | comment | added | Carlo Beenakker | @Marcel --- I presume these papers you are referring to all interpret "normal" as "Gaussian" --- which is a different kettle of fish --- for complex normal matrices I would just draw a random unitary $U$ and a random diagonal matrix $D$ and write $A=UDU^\dagger$ --- no idea how to impose the constraint that $A$ is real... | |
| Aug 31, 2017 at 20:57 | comment | added | Marcel | There are many papers about "random normal matrices". Have you googled this? | |
| Aug 31, 2017 at 20:54 | comment | added | Nate Eldredge | "Random" only makes sense when you specify a probability distribution. Which one do you want? There isn't any canonical choice, AFAIK. | |
| Aug 31, 2017 at 19:53 | review | First posts | |||
| Aug 31, 2017 at 20:06 | |||||
| Aug 31, 2017 at 19:50 | history | asked | Domin | CC BY-SA 3.0 |