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...
49 KB (7,081 words) - 12:21, 14 June 2024
covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions...
37 KB (5,794 words) - 14:53, 1 January 2025
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...
11 KB (1,436 words) - 14:39, 13 December 2024
of aggregate random variables, e.g. a random matrix, random tree, random sequence, stochastic process, etc. Formally, a multivariate random variable is...
21 KB (3,426 words) - 01:02, 31 July 2024
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...
8 KB (768 words) - 22:33, 3 December 2023
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...
5 KB (363 words) - 04:07, 6 August 2024
Wishart distribution (redirect from Wishart matrix)
the distribution in 1928. Other names include Wishart ensemble (in random matrix theory, probability distributions over matrices are usually called "ensembles")...
27 KB (4,206 words) - 04:50, 21 November 2024
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...
7 KB (1,032 words) - 23:15, 18 April 2023
In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows...
108 KB (13,476 words) - 09:46, 2 January 2025
theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a...
45 KB (5,041 words) - 21:18, 27 October 2024
generated free groups have the same elementary theory. Later connections to random matrix theory, combinatorics, representations of symmetric groups, large deviations...
6 KB (691 words) - 03:11, 11 March 2024
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...
22 KB (2,731 words) - 05:51, 24 October 2024
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...
6 KB (889 words) - 21:29, 30 July 2024
ISBN 978-1108120494. Asymptotic safety in quantum gravity Cavity method Euclidean random matrix Parisi–Sourlas stochastic quantization procedure p-adic quantum mechanics...
23 KB (1,961 words) - 14:53, 8 January 2025
distribution to matrix-valued random variables. The probability density function for the random matrix X (n × p) that follows the matrix normal distribution...
10 KB (1,669 words) - 23:10, 18 December 2024
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...
13 KB (1,515 words) - 17:06, 29 December 2024
functions of a matrix argument have applications in random matrix theory. For example, the distributions of the extreme eigenvalues of random matrices are...
4 KB (719 words) - 17:15, 14 April 2022
normal complex random vectors that are circularly symmetric are of particular interest because they are fully specified by the covariance matrix Γ {\displaystyle...
16 KB (2,288 words) - 00:08, 11 May 2024
In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices...
25 KB (3,930 words) - 21:12, 2 August 2024
e.g. a random matrix, random tree, random sequence, random process, etc. A random matrix is a matrix-valued random element. Many important properties...
13 KB (1,890 words) - 19:13, 13 October 2023
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...
36 KB (4,826 words) - 18:19, 27 December 2024
numerical linear algebra, computational science, parallel computing, and random matrix theory. He is one of the creators of the technical programming language...
8 KB (763 words) - 07:37, 13 September 2024
covariance matrix is called the precision matrix, denoted by Q = Σ − 1 {\displaystyle {\boldsymbol {Q}}={\boldsymbol {\Sigma }}^{-1}} . A real random vector...
65 KB (9,518 words) - 19:55, 6 January 2025
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...
7 KB (1,237 words) - 17:13, 21 April 2024
Random element Random field Random function Random graph Random matrix Random measure Random multinomial logit Random naive Bayes Random permutation statistics...
87 KB (8,285 words) - 04:29, 7 October 2024
List of named matrices (redirect from List of matrix)
Correlation matrix — a symmetric n×n matrix, formed by the pairwise correlation coefficients of several random variables. Covariance matrix — a symmetric...
32 KB (1,336 words) - 16:53, 5 November 2024
distribution of the eigenvalues of many random symmetric matrices, that is, as the dimensions of the random matrix approach infinity. The distribution of...
8 KB (988 words) - 12:41, 7 October 2024
Isotropic position (category Matrix stubs)
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...
2 KB (246 words) - 06:14, 19 September 2024
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...
17 KB (1,687 words) - 11:18, 8 January 2025
Terence Tao (section Random matrices)
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...
79 KB (6,683 words) - 20:58, 1 January 2025