Timeline for On the equation $[U, V] - V_x = C(x)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 23, 2021 at 4:09 | vote | accept | Talmsmen | ||
| May 18, 2021 at 9:26 | comment | added | Robert Bryant | @JPwin: Unless $U$ takes values in a solvable Lie subalgebra of ${\frak{gl}}(n,\mathbb{R})$ there is no algorithmic way to solve the equation $M_x = - MU$, unfortunately. The so-called 'time-ordered exponential' is just the formalization of the limit of Euler's method for solving the equation numerically. For a specific $U$, one can sometimes (though not very often, it has to be admitted) find an explicit solution using differential Galois theory. | |
| May 18, 2021 at 3:58 | comment | added | Talmsmen | Thank you for your excellent answer. How would one go about finding a solution to $M_x = -MU$? I originally hoped to write $X(x) = Ce^{-\int M(x) dx}$ but was later told that the lack of commutativity for matrix multiplication causes the chain rule to break down. Would I have to use a Magnus series or consider the system as a time-ordered exponential? Thank you again for all of your help. | |
| May 17, 2021 at 16:42 | vote | accept | Talmsmen | ||
| May 23, 2021 at 4:09 | |||||
| May 17, 2021 at 10:37 | history | answered | Robert Bryant | CC BY-SA 4.0 |