# Matrix variate probability distribution

As matrixvariate probability distributions is known in the stochastic those probability measures , on the premises of matrices are defined. They appear as distributions of random matrices .

From a measure theoretical point of view , matrix-variable probability distributions do not differ from multivariate probability distributions . This is because that the measurable amounts on the measurable quantities are identified. For the assignment of the probabilities it is therefore irrelevant whether it is a matrix with rows and columns or a vector of length . ${\ displaystyle \ mathbb {R} ^ {n \ times k}}$${\ displaystyle \ mathbb {R} ^ {nk}}$${\ displaystyle n}$${\ displaystyle k}$${\ displaystyle nk}$

However, due to the additional algebraic structure, matrix-variable probability distributions also allow algebraic questions to be investigated with stochastic approaches. In this way questions can be investigated like

• the entries in a matrix are evenly distributed in the interval from zero to one. How are the eigenvalues distributed?
• What is the probability that the matrix is ​​invertible?