Timeline for Why does the $L_2$ norm give the shortest path between 2 points?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 7 at 15:02 | comment | added | Er Jio | The equation you wrote, $||{\bf v}|| = \sum^N ||\frac{\bf v}{N}|| = N\cdot||\frac{\bf v}{N}||$ follows from absolute homogeneity, $||\alpha{\bf v}|| = |\alpha|\cdot||{\bf v}||$. This is a property of all norms, not just $L_1,L_2$. | |
| May 4, 2020 at 4:35 | comment | added | user237040 | This is wrong, that equation holds for every $p \neq 0$. | |
| Sep 27, 2014 at 21:21 | comment | added | CuriousKev | @hjfreyer I consider the inability to look at a path piecewise much more damning that the issue with rotational symmetry. Because of this, I'm not sure what would even be the appropriate way to discuss transformations of paths, but it would have to be very non-linear (for example we can't use linear algebra, with transformation matrices, if you'd hope to find a transformation that preserves L3). | |
| Sep 27, 2014 at 20:53 | comment | added | hjfreyer | Yeah, I'd assumed rotational symmetry was important. Out of curiosity, are there other vector transformations that preserve the L3 norm, but not L2? | |
| Sep 27, 2014 at 20:43 | vote | accept | hjfreyer | ||
| Sep 27, 2014 at 1:34 | review | First posts | |||
| Sep 27, 2014 at 1:35 | |||||
| Sep 27, 2014 at 1:29 | history | answered | CuriousKev | CC BY-SA 3.0 |