Timeline for Mapping a subset of semi-definite matrices through arcsinus
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 19, 2012 at 16:44 | comment | added | Robert Israel | Here are the plots: 3 x 3 math.ubc.ca/~israel/problems/phi3.jpg 4 x 4 math.ubc.ca/~israel/problems/phi4.jpg | |
| Apr 19, 2012 at 16:23 | comment | added | Robert Israel | I looked at Toeplitz matrices of the form $$M(s,t) = \pmatrix{1 & s & t & 0\cr s & 1 & s & t\cr t & s & 1 & s\cr 0 & t & s & 1\cr}$$ and plotted the region in the $(s,t)$ plane where $\Phi^{-1}(M)(s,t)$ is SDP. It turned out not to be convex. The $3 \times 3$ case was convex. | |
| Apr 19, 2012 at 7:01 | comment | added | kaleidoscop | Thank you! Did you try with $3\times 3$ matrices? How did you find this example? | |
| Apr 19, 2012 at 7:01 | vote | accept | kaleidoscop | ||
| Apr 18, 2012 at 22:56 | history | edited | Robert Israel | CC BY-SA 3.0 |
added 1 characters in body
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| Apr 18, 2012 at 18:44 | history | answered | Robert Israel | CC BY-SA 3.0 |
