Timeline for Eigenvectors of $P^\top P$ for 0/1 matrices $P$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 14 at 21:41 | answer | added | Eric Neyman | timeline score: 3 | |
| Jul 13 at 1:55 | comment | added | Eric Neyman | The issue is that $\mathbf{1}$ has length N, not m, so the inequality should have an N, not an m. | |
| Jul 13 at 0:59 | comment | added | Mark Schultz-Wu | By multiplying on the left by $\mathbf{u}^t$, I get the condition $\lambda \lVert \mathbf{u}\rVert_2 = \lVert P\mathbf{u}\rVert_2$, and then CS-inequality gives $$ \langle \mathbf{u}, \mathbf{1}\rangle^2 \leq m\lVert \mathbf{u}\rVert_2^2 = \frac{m}{\lambda^2}\lVert P\mathbf{u}\rVert_2^2. $$ Seems plausible some operator norm bound on $P$ will finish things off, but I don't have time to think about it now. | |
| S Jul 13 at 0:27 | review | First questions | |||
| Jul 13 at 6:23 | |||||
| S Jul 13 at 0:27 | history | asked | Eric Neyman | CC BY-SA 4.0 |