  A Lyapunov matrix equation can be converted, by using the Jordan
decomposition theorem for matrices, into an equivalent Lyapunov matrix equation
where the matrix is a Jordan matrix. The Lyapunov matrix equation with Jordan
matrix can be reduced to a system of Sylvester-Lyapunov type matrix equations.
We completely solve the Sylvester-Lyapunov type matrix equations corresponding
to the Jordan block matrices of the initial matrix.
