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...

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

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...

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

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

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

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...

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

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

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...

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...

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...

and uniformly bounded random variables. In the matrix setting, the analogous theorem concerns a sum of positive-semidefinite random matrices subjected to...

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...

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...

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

computation, and random matrix theory, a probability distribution over vectors is said to be in isotropic position if its covariance matrix is equal to the...

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

}})^{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...

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 = [...

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...

normal complex random vectors that are circularly symmetric are of particular interest because they are fully specified by the covariance matrix Γ {\displaystyle...

matrix. In multivariate statistics and probability theory, the scatter matrix is a statistic that is used to make estimates of the covariance matrix,...

and measurements of a quantum circuit. The idea is similar to that of random matrix theory which is to use the QRC to obtain almost exact results of non-integrable...

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

The Matrix is a 1999 science fiction action film written and directed by the Wachowskis. It is the first installment in the Matrix film series, starring...

In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely...