# 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 .

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?

## Web links

- AK Gupta: Matrix variate distribution . In: Michiel Hazewinkel (Ed.): Encyclopaedia of Mathematics . Springer-Verlag , Berlin 2002, ISBN 978-1-55608-010-4 (English, online ).