Timeline for real symmetric matrix has real eigenvalues - elementary proof
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 26, 2017 at 6:38 | comment | added | Jan Peter Schäfermeyer | According to Folkmar Bornemann, this proof is due to Herbert Wilf | |
| S Nov 17, 2015 at 4:48 | history | edited | Omar Antolín-Camarena | CC BY-SA 3.0 |
Corrections
|
| S Nov 17, 2015 at 4:48 | history | suggested | BigM | CC BY-SA 3.0 |
Corrections
|
| Nov 17, 2015 at 4:37 | review | Suggested edits | |||
| S Nov 17, 2015 at 4:48 | |||||
| Jan 14, 2013 at 4:29 | comment | added | Mariano Suárez-Álvarez | This feels so wrong! :-) | |
| Jan 13, 2013 at 14:21 | comment | added | Marcos Cossarini | I meant $\frac 12\sum a_{ij}^2$. | |
| Jan 13, 2013 at 2:00 | comment | added | Marcos Cossarini | To add a little more detail: The total energy $\frac 12\sum a_{ij}$, which is the sum of the energy on the diagonal and $\Sigma$, is invariant by orthogonal conjugation, so we want to move it to the diagonal. When you apply a rotation $J$ in the plane spanned by the canonic vectors $e_i$ and $e_j$, which only affects the $i$th and $j$th rows and columns, the resulting coefficients $ii$, $ij$, $ji$, $jj$ of $J^tAJ$ depend only on the same coefficients of $A$, so the problem is reduced to increasing the energy on the diagonal of a $2\times 2$ matrix. | |
| Jan 11, 2013 at 18:16 | history | edited | Uwe Franz | CC BY-SA 3.0 |
added 11 characters in body
|
| Jan 11, 2013 at 17:24 | history | edited | Uwe Franz | CC BY-SA 3.0 |
added 39 characters in body
|
| Jan 11, 2013 at 17:08 | history | edited | Uwe Franz | CC BY-SA 3.0 |
edited body; added 33 characters in body
|
| Jan 11, 2013 at 17:02 | history | edited | Uwe Franz | CC BY-SA 3.0 |
added 168 characters in body; added 11 characters in body
|
| Jan 11, 2013 at 16:18 | history | answered | Uwe Franz | CC BY-SA 3.0 |