Timeline for Prove/disprove a linear algebra inequality
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 12, 2023 at 11:41 | comment | added | Chen Zeno | Thank you for the answer! | |
| Jun 12, 2023 at 8:12 | comment | added | user42355 | Very nice! So essentially, if $u_i^T a > 0$ for every $i$, then you prove $\sum_i (u_i^T a) (u_i^T w) \le \frac{1 + a^T w}{2}$, and for a general $a$, applying this for $a$ and $-a$ for the relevant $u_j$'s, and summing up, we get the upper bound $\frac{1 + a^T w}{2} + \frac{1 - a^T w}{2} = 1$. | |
| Jun 12, 2023 at 6:59 | comment | added | jmd | Thanks, I corrected it. I meant "for $i\neq j$". | |
| Jun 12, 2023 at 6:53 | history | edited | jmd | CC BY-SA 4.0 |
edited body
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| Jun 12, 2023 at 5:37 | history | edited | jmd | CC BY-SA 4.0 |
edited body
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| Jun 12, 2023 at 3:31 | comment | added | Iosif Pinelis | The condition $u_i^T u_j \leq 0$ for all $i,j$ can only hold if $u_i=0$ for all $i$. | |
| Jun 11, 2023 at 23:41 | history | edited | jmd | CC BY-SA 4.0 |
added 55 characters in body
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| Jun 11, 2023 at 23:10 | history | answered | jmd | CC BY-SA 4.0 |