Timeline for Proof negative-definiteness of a nonsymmetric and rank-deficient matrix
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2021 at 9:44 | comment | added | Beram | thanks, didn't know about CVX yet! Seems powerful | |
| Feb 5, 2021 at 0:36 | comment | added | Nathaniel Johnston | For $N = 2$, you can basically type the problem as-is into CVX in MATLAB. Just tell it what your objective function is and then specify the constraint $\mathbf{a}\mathbf{b}^T + \mathbf{b}\mathbf{a}^T \leq 0$, where $\leq 0$ here means negative semidefinite. | |
| Feb 4, 2021 at 21:30 | comment | added | Beram | ok, thanks, I thought so. But what do I need to do for $N=2$? | |
| Feb 3, 2021 at 15:31 | comment | added | Nathaniel Johnston | As you noted, if $N > 2$ then your matrix $C$ is never negative definite (e.g., if $\mathbf{v}$ is orthogonal to $\mathbf{a}$ and $\mathbf{b}$ then $\mathbf{v}^TC\mathbf{v} = 0$). Is it not enough for your $C$ to be negative semidefinite? If semidefiniteness is OK, then this type of problem can be solved via semidefinite programming solvers (SeDuMi etc, or frameworks like CVX for MATLAB). | |
| Feb 2, 2021 at 17:18 | review | First posts | |||
| Feb 3, 2021 at 3:44 | |||||
| Feb 2, 2021 at 17:10 | history | asked | Beram | CC BY-SA 4.0 |