Timeline for Conditions for including cones
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 4, 2023 at 13:34 | comment | added | Iosif Pinelis | @NathanielJohnston : Thank you for your comment. | |
| May 3, 2023 at 20:33 | comment | added | Nathaniel Johnston | @IosifPinelis - Very nice! $N = 3$ isn't possible, so your construction is optimal. What's also kind of neat about your $N = 4$ example is that, even though they can't be rotated into the positive orthant of $\mathbb{R}^3$, they can be embedded into higher-dimensional space (e.g., by appending $0$ coordinates) and rotated into the positive orthant in that space (I think dimension $6$ suffices). Contrast that with my set of $N = 5$ vectors that can't be rotated into the positive orthant in any dimension. | |
| May 3, 2023 at 19:34 | comment | added | Iosif Pinelis | @NathanielJohnston : It is now shown within the same framework that it is enough to have $N=4$ points, which cannot be further improved. | |
| May 2, 2023 at 15:52 | comment | added | Iosif Pinelis | @NathanielJohnston : You wrote: "for $N$ very large". Actually, $N$ does not have to be very large using that method. It is now shown in the Added paragraph that one can take $N=14$ (or maybe even $<14$. | |
| May 2, 2023 at 10:53 | comment | added | Nathaniel Johnston | @dzk - I'm not aware of any books other than the one that I linked. | |
| May 1, 2023 at 18:00 | comment | added | dzk | May I ask which relevant books are there? Thank you | |
| May 1, 2023 at 17:53 | comment | added | Iosif Pinelis | Wow, I had never heard about completely positive matrices or even suspected they were a thing! Thank you for this information. | |
| May 1, 2023 at 17:34 | history | answered | Nathaniel Johnston | CC BY-SA 4.0 |