mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability...

covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions...

of aggregate random variables, e.g. a random matrix, random tree, random sequence, stochastic process, etc. Formally, a multivariate random variable is...

subspace. Random projection is computationally simple: form the random matrix "R" and project the d × N {\displaystyle d\times N} data matrix X onto K...

In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows...

an N×N Euclidean random matrix  is defined with the help of an arbitrary deterministic function f(r, r′) and of N points {ri} randomly distributed in a...

the distribution in 1928. Other names include Wishart ensemble (in random matrix theory, probability distributions over matrices are usually called "ensembles")...

a cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random vector and j-th element...

cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors. The...

distribution to matrix-valued random variables. The probability density function for the random matrix X (n × p) that follows the matrix normal distribution...

functions of a matrix argument have applications in random matrix theory. For example, the distributions of the extreme eigenvalues of random matrices are...

The ranked eigenvalues En from these random matrices obey Wigner's semicircular distribution: For a N×N matrix the average density for eigenvalues of...

named for Freeman Dyson. Dyson studied this process in the context of random matrix theory. There are several equivalent definitions: Definition by stochastic...

are positive. The matrix J {\displaystyle J} is also known as the community matrix. May supposed that the Jacobian was a random matrix whose off-diagonal...

general class of random matrix products, the norm grows as λn, where n is the number of factors. Their results apply to a broad class of random sequence generating...

e.g. a random matrix, random tree, random sequence, random process, etc. A random matrix is a matrix-valued random element. Many important properties...

theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a...

generated free groups have the same elementary theory. Later connections to random matrix theory, combinatorics, representations of symmetric groups, large deviations...

random vectors of the Student's t-distribution, which is a distribution applicable to univariate random variables. While the case of a random matrix could...

is a British mathematician at the University of Bristol working in random matrix theory and quantum chaos. Snaith was educated at the University of Bristol...

rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

covariance matrix is called the precision matrix, denoted by Q = Σ − 1 {\displaystyle {\boldsymbol {Q}}={\boldsymbol {\Sigma }}^{-1}} . A real random vector...

Correlation matrix — a symmetric n×n matrix, formed by the pairwise correlation coefficients of several random variables. Covariance matrix — a symmetric...

numerical linear algebra, computational science, parallel computing, and random matrix theory. He is one of the creators of the technical programming language...

statistics, information and communication sciences with a special focus on random matrix theory and learning algorithms. In the AI field, he is known for his...

}})^{2},\alpha (1+{\sqrt {\lambda }})^{2}].} This law also arises in random matrix theory as the Marchenko–Pastur law. Its free cumulants are equal to...

study of non-symmetric random matrices. They showed that if n is large and the entries of a n × n matrix A are selected randomly according to any fixed...

random vector, sample covariance matrices are positive semi-definite. To prove it, note that for any matrix A {\displaystyle \mathbf {A} } the matrix...

In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices...