Magnus expansion

Summary

The Magnus expansion writes the solution of a linear system $Y' = A(t)\, Y$, $Y(0) = I$, as one matrix exponential $Y(t) = e^{\Omega(t)}$. The exponent $\Omega(t)$ is a series of iterated integrals of commutators of $A$ at different times. When the matrices $A(t)$ commute with each other, only the first term $\int_0^t A$ remains. Truncations of the series keep structure, for example they stay in a matrix group, which makes them useful in numerical methods and quantum mechanics. See the definition.