  In this paper, based on an optimization problem, a sketch-and-project method
for solving the linear matrix equation AXB = C is proposed. We provide a
thorough convergence analysis for the new method and derive a lower bound on
the convergence rate and some convergence conditions including the case that
the coefficient matrix is rank deficient. By varying three parameters in the
new method and convergence theorems, the new method recovers an array of
well-known algorithms and their convergence results. Meanwhile, with the use of
Gaussian sampling, we can obtain the Gaussian global randomized Kaczmarz
(GaussGRK) method which shows some advantages in solving the matrix equation
AXB = C. Finally, numerical experiments are given to illustrate the
effectiveness of recovered methods.
