Timeline for Interpreting positive semidefinite matrix as a graph
Current License: CC BY-SA 4.0
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| Apr 26 at 19:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 1 at 11:49 | comment | added | David Roberson | If you replace a solution $X$ with $\Phi(X)$ where $\Phi$ is the projection onto the coherent algebra generated by $A_1, \ldots, A_n$, then $\mathcal{A}(X)$ does not change and $\Phi$ also preserves positivity. So you can restrict your search to matrices in the coherent algebra generated by $A_1, \ldots, A_n$. If this happens to be an association scheme, then the positivity condition can be replaced by linear constraints. | |
| Jan 23 at 5:15 | comment | added | mathoverflowUser | You might want to look into the work of Miroslav Fiedler, espacially chapter 6.1 and 6.2 of his book "Matrices and Graphs in Geometry" where he assigns to graphs the Laplacian (a positive semidefinite matrix) and conversely to a simplex given by a positive definite matrix he asssigns a graph. | |
| Jan 23 at 4:12 | comment | added | Abhishek Halder | You may find Ch. 9 of this reference helpful: seas.ucla.edu/~vandenbe/publications/chordalsdp.pdf | |
| Jan 23 at 3:18 | history | edited | patchouli | CC BY-SA 4.0 |
added 9 characters in body
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| Jan 23 at 2:52 | history | asked | patchouli | CC BY-SA 4.0 |