Timeline for For positive definite $A,B$ why does $AB+BA$ tend to be positive definite?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2022 at 1:07 | history | edited | Michael Hardy | CC BY-SA 4.0 |
The reason for the conspicuous lack of proper spacing here is that unlike \operatorname, \text lacks context-dependent spacing
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| Aug 5, 2016 at 0:39 | comment | added | Robert Israel | Good suggestion: changed $S$ and $T$ to $X$ and $Y$. | |
| Aug 5, 2016 at 0:38 | history | edited | Robert Israel | CC BY-SA 3.0 |
edited body
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| Aug 4, 2016 at 23:14 | comment | added | Gerry Myerson | May I suggest not using the symbol $T$ two different ways in one equation? | |
| Aug 4, 2016 at 22:19 | comment | added | Jean Marie Becker | I just add a proof for the reader that might be puzzled by your first formula. It is based (I imagine that it is also your way for proving it) on the following lemma (known as invariance by cylic permutations) $tr(MNP)=tr(PMN)=tr(NPM)$ for any square matrices with the same dimensions. Thus it suffices to write $AB=A^{1/2}A^{1/2}B=A^{1/2}BA^{1/2}$, and the same for $BA$. | |
| Aug 4, 2016 at 21:54 | vote | accept | Albert Nagi | ||
| Aug 4, 2016 at 21:14 | history | answered | Robert Israel | CC BY-SA 3.0 |