  Krylov methods have reappeared recently, connecting physically sensible
notions of complexity with quantum chaos and quantum gravity. In these
developments, the Hamiltonian and the Liouvillian are tridiagonalized so that
Schrodinger/Heisenberg time evolution is expressed in the Krylov basis. In the
context of Schrodinger evolution, this tridiagonalization has been carried out
in Random Matrix Theory. We extend these developments to Heisenberg time
evolution, describing how the Liouvillian can be tridiagonalized as well until
the end of Krylov space. We numerically verify the analytical formulas both for
Gaussian and non-Gaussian matrix models.
