Timeline for Eigenvalue problem with two quadratic constraints
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2017 at 21:48 | comment | added | Igor Rivin | @ChristianRemling Re your first comment, I was tired :( Re the second, I am specifically looking at the OP's lagrange multiplier equation. | |
| Nov 12, 2017 at 21:44 | comment | added | Christian Remling | I don't understand your second sentence: $x^tBx=0$ does not imply that $x\in N(B)$ (for example take $B=\textrm{diag}(1,-1)$). | |
| Nov 12, 2017 at 21:36 | comment | added | Yang | Thank you for the comments. In viewing of your comments, I removed the "full rank" condition to accept a broader class of solutions. One obviously can use the vectors in the null space of $B$ to minimize $A$. If $B$ is not symmetric, are there any additional solutions beyond the null-space? I appreciate your answer. | |
| Nov 12, 2017 at 14:51 | comment | added | Igor Rivin | @FedericoPoloni I said "rarely" not never. | |
| Nov 12, 2017 at 10:04 | comment | added | Federico Poloni | Why "$x^TBx$ is rarely zero for full-rank matrices"? For instance, the block matrix $\begin{bmatrix}0 & I\\I & 0\end{bmatrix}$ has two dim/2-dimensional subspaces of vectors such that $x^TBx=0$. | |
| Nov 12, 2017 at 5:04 | history | answered | Igor Rivin | CC BY-SA 3.0 |