As per the title, I'd like to calculate the exponential of a matrix which has an antihermitian component and a symmetric component (although this fact may not be useful). More specifically
$\mathbf{M}=\begin{pmatrix}ia&b+ic\\b+ic&id\end{pmatrix}$
I have in front of me the solutions for the case that $b = 0$ (antihermitian) and the case for $a,c,d = 0$ (symmetric), but not for $\mathbf M$. Does anyone know of a convenient form for calculating this?
Perhaps I should elaborate; computing by various methods is not a problem, but I'm wondering if there is a convenient set of formulae for this as there are for, say, the real case. To further elaborate, I've used a formula for convenience in the case of $\exp (-i\mathbf{H}t)$, where $\mathbf{H}t$ is Hermitian many times to solve the Schrödinger equation. This is really just to expedite calculations, since it's a waste of my time to do it the long way. I'm now working with dissipative systems a lot, and one way to handle them is with what is referred to as a non-hermitian Hamiltonian. That's where this question comes in.