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A random matrix is a matrix whose entries consist of random variables from some specified distribution. Random matrices have many modern applications in physics, finance, statistics and numerical analysis.
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Why the matrix normal distribution is not estimated with this "method of moments"?
According to the Wikipedia Page, a random matrix $\bf{X}\in \mathbb{R}^{p\times q}$ follows a matrix normal distribution $\cal{MN}(\bf M, \bf U, \bf V)$ means that
$$ \text{vec}(\bf X) \sim \cal N ( \ …