  In this paper, we study the log-likelihood function and Maximum Likelihood
Estimate (MLE) for the matrix normal model for both real and complex models. We
describe the exact number of samples needed to achieve (almost surely) three
conditions, namely a bounded log-likelihood function, existence of MLEs, and
uniqueness of MLEs. As a consequence, we observe that almost sure boundedness
of log-likelihood function guarantees almost sure existence of an MLE, thereby
proving a conjecture of Drton, Kuriki and Hoff. The main tools we use are from
the theory of quiver representations, in particular, results of Kac, King and
Schofield on canonical decomposition and stability.
