Timeline for Eigenvalues of certain positive matrices
Current License: CC BY-SA 3.0
5 events
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| Aug 18, 2011 at 14:46 | comment | added | Mikael de la Salle | One additional remark: the condition that $s_i s_{n+1-i}$ is constant is also a sufficient condition for the existence of such $Q$, in which case $Q$ can even be a matrix with real entries. This follows from the easy fact that, for any $s>0$, there is a real 2 by 2 matrix $Q_s$ such that $Q_s^2=1$ and $Q_s^* Q_s$ is diagonal with diagonal entries $s,1/s$. Indeed, if $s_i s_{n+1-i}=1$, the block diagonal matrix with blocks $Q_{s_1},\dots,Q_{s_{[n/2]}}$ (and $1$ if $n$ is odd) does the job. | |
| Aug 18, 2011 at 14:01 | comment | added | gloerchen | Fine, nice answer! | |
| Aug 18, 2011 at 13:55 | vote | accept | gloerchen | ||
| Aug 18, 2011 at 13:38 | history | edited | alext87 | CC BY-SA 3.0 |
added 3 characters in body
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| Aug 18, 2011 at 13:33 | history | answered | alext87 | CC BY-SA 3.0 |