Timeline for Lipschitz continuity of eigenvalues and eigenvectors of Hermitian matrices
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 6, 2021 at 6:21 | comment | added | YCor | @MichaelMontgomery still this answers the question, since the question was to find a determination as a function of $A$. But your other example exhibits another, local, obstruction. | |
| Jun 6, 2021 at 6:18 | comment | added | YCor | In this example, $v_+$, $v_-$ can be chosen continuously as function of $\phi$, but not as a continuous function of $A$. Indeed as a function of $A=A(\phi)$, we would get $v_+(A(\phi+2\pi))=-v_+(A(\phi))$. So there is no continuous determination, but there is continuous determination along paths (which more generally holds when multiplicities of eigenvalues are fixed). | |
| Jun 6, 2021 at 4:12 | comment | added | Michael Montgomery | This example has a continuous choice of eigenvectors, $v_+=(\cos(\phi/2),\sin(\phi/2))$ and $v_+=(-\sin(\phi/2),\cos(\phi/2))$. | |
| Jun 5, 2021 at 18:49 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |