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 of numbers or other mathematical objects with elements or entries arranged in rows and...

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...

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")...

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...

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

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...

In random matrix theory, the Gaussian ensembles are specific probability distributions over self-adjoint matrices whose entries are independently sampled...

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

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...

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

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 = [...

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

random matrix theory introduced by Craig Tracy and Harold Widom (1993, 1994). It is the distribution of the normalized largest eigenvalue of a random...

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...

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

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...

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...

}})^{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...

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

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...

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

the distribution would agree with the distribution of spacings of GUE random matrix eigenvalues using Cray X-MP. In 1987 he reported the calculations in...

born out of a desire to quantify spectral features of complex systems. Random matrix theory was developed in an attempt to characterize spectra of complex...