Timeline for Index of a function and a gradient flow
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 28, 2016 at 17:38 | history | edited | hardmath | CC BY-SA 3.0 | fix broken link |
| Jul 7, 2014 at 6:20 | vote | accept | Martin Wang | ||
| Jul 7, 2014 at 5:33 | vote | accept | Martin Wang | ||
| Jul 7, 2014 at 5:33 | |||||
| Jul 7, 2014 at 3:16 | comment | added | user147263 | @MartinWang Okay, I clarified the answer. | |
| Jul 7, 2014 at 3:15 | history | edited | user147263 | CC BY-SA 3.0 | added 401 characters in body |
| Jul 7, 2014 at 1:15 | comment | added | Martin Wang | Actually, it's called Morse Index. In my understanding, when considering a function $F(X)$, the morse index at critical point is number of negative eigen values of hessian matrix. however, when considering a gradient flow $X'=F(X)$, the morse index is defined as number of positive eigen values. | |
| Jul 7, 2014 at 1:01 | comment | added | Martin Wang | It's still the number of negative eigen values of $D^2F(x_0)$. A sink in the sense of vector field is corresponding to the index $2$, which is not literally consistent with the sink concept by intuition. | |
| Jul 6, 2014 at 17:25 | comment | added | user147263 | @MartinWang In the question you have two versions of index: the first one gives 0 for a sink, the other gives 2. What is the definitions of the second one? | |
| Jul 6, 2014 at 17:22 | comment | added | Martin Wang | Both indices are index of $F$ at critical point $x_0$, i.e. number of negative eigen values of $D^2F(x_0)$. I don't mention the degree/index of a vector field stationary point. | |
| Jul 6, 2014 at 14:43 | history | answered | user147263 | CC BY-SA 3.0 |