# Solving the Lindblad quantum master equation in matrix form

I have just started learning density matrix and quantum master equations, and I am given a problem set that asks to find the solution to the Lindblad equation with $$H$$, $$L_+$$, $$L_-$$, $$L_z$$, and $$\rho(0)$$ given in the matrix form.

The thing is, I know how to solve a system of linear differential equations such as Schrödinger equations to find a vector solution, but not a matrix equation with a matrix solution. Can anybody give me a hint or a link to the steps, because I think I am too dumb to find any, having searched the web and the library for about half the day.

• The master equation is a system of linear, ordinary differential equations (ODEs) for the components of the density matrix (write them out explicitly!). If it helps, you could even collect these density matrix components into a vector... – Mark Mitchison Mar 20 '18 at 15:27
• physics.stackexchange.com/q/115066 Im guessing what you mean by collect components into a vector is in the answer provided in the link above. Thanks anyways – Jin Mar 20 '18 at 15:34

• $\uparrow$ Link? – Qmechanic May 18 '18 at 11:16