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...derson, G.W.; Guionnet, A.; Zeitouni, O. (2010). An introduction to random matrices. Cambridge: Cambridge University Press. {{isbn|978-0-521-19452-5}}.</ref> ..., 323–346</ref><ref>Voiculescu, D., Multiplication of certain noncommuting random variables, J. Operator Theory 18 (1987), 2223–2235</ref> ...

...''circular symplectic ensemble''' (CSE) on self dual unitary quaternionic matrices. ...if ''U'' is a random element of CUE(''2n''), then ''U^RU'' is a random element of CSE(''n''), where ...

...hematician)|Dan Voiculescu]].<ref>D. Voiculescu, K. Dykema, A. Nica, "Free Random Variables", CIRM Monograph Series, AMS, Providence, RI, 1992</ref> The defi ...r example may be <math>A=M_N</math>, the algebra of <math>N\times N</math> matrices with the functional given by the normalized trace <math>\phi=\frac{1}{N}Tr< ...

...is an {{nobr|(''N'' + 1) × (''N'' + 1)}} matrix. The first few Krawtchouk matrices are: ...first2=J. |date=2007 |title=Krawtchouk matrices from classical and quantum random walks |eprint=quant-ph/0702173}}</ref> ...

...stribution]] over [[Positive-definite matrix|positive definite]] symmetric matrices with unit diagonals.<ref name="bda">{{Cite book |last1=Gelman |first1=Andre ...orota|last3=Joe|first3=Harry|year=2009|title=Generating Random Correlation Matrices Based on Vines and Extended Onion Method|journal=Journal of Multivariate An ...

...ier }}</ref> The surmise was a result of Wigner's introduction of [[random matrices]] in the field of [[nuclear physics]]. The surmise consists of two postulat ...ices <math> M</math>, with elements that are independent standard gaussian random variables, with joint distribution proportional to ...

...; ''n''}} [[random matrix]] with [[independent and identically distributed random variables|independent and identically distributed entries]] in the limit ...'}} matrices]] whose entries are [[independent and identically distributed random variables]], all with [[expected value|mean]] zero and [[variance]] equal t ...

...he ''i''-th element of a [[random vector]] and ''j''-th element of another random vector. When the two random vectors are the same, the cross-covariance matrix is referred to as [[covar ...

In the fields of [[machine learning]], the [[theory of computation]], and [[random matrix theory]], a probability distribution over vectors is said to be in ' * {{cite journal |first=M. |last=Rudelson |title=Random Vectors in the Isotropic Position |journal=[[Journal of Functional Analysis ...

...d J. Tanner "Improved Bounds on Restricted Isometry Constants for Gaussian Matrices"</ref> Web forms to evaluate bounds for the Gaussian ensemble are available ...ved by computing the exact probability that all the eigenvalues of Wishart matrices lie within an interval. ...

...rt description|Distribution of singular values of large rectangular random matrices}} ...ehavior of [[singular value]]s of large rectangular [[random matrix|random matrices]]. The theorem is named after [[Soviet Union|Soviet]] [[Ukrainians|Ukraini ...

...verse gamma distribution]] to [[Positive-definite matrix|positive-definite matrices]].<ref name="iranmanesha">{{cite journal |last=Iranmanesha |first=Anis |fir [[Category:Random matrices]] ...

...the [[gamma distribution]] to [[Positive-definite matrix|positive-definite matrices]].<ref name="iranmanesh">Iranmanesh, Anis, M. Arashib and S. M. M. Tabataba [[Category:Random matrices]] ...

...vector. Complex random variables can always be considered as pairs of real random vectors: their real and imaginary parts. ...on|mean]] of a complex random vector. Other concepts are unique to complex random vectors. ...

...hang equation|KPZ-universality]] with the theory of [[random matrix|random matrices]]. ...On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations |date=1998 |eprint=math/9810105}}</ref><ref>{{cite book | doi= ...

Consider the space of <math display="inline">n\times n</math> Hermitian matrices with all eigenvalues distinct. ...al |last=Tao |first=Terence |last2=Vu |first2=Van |date=2011 |title=Random matrices: Universality of local eigenvalue statistics |url=http://projecteuclid.org/ ...

{{Short description|Statistical distribution of complex random variables}} ...</math> or <math>\mathcal{N}_{\mathcal{C}}</math>, characterizes [[complex random variable]]s whose real and imaginary parts are jointly [[Multivariate norma ...

support = <math>p\times p</math> matrices with both <math>U</math> and <matH>I_p-U</math> [[positive definite]]| Also, if <math>H</math> is a random orthogonal <math>p\times p</math> matrix which is [[independence (probabili ...

...[Hadamard product (matrices)|Hadamard product]] of two [[positive definite matrices]] is also a positive definite matrix. ...duct <math>M \circ N</math> is positive definite for all positive definite matrices <math>N</math>, then <math>M</math> itself is positive definite. ...

...at { ''f''_''i'' } is an indexed collection of [[Random variable|random variables]], that is, a stochastic process. Let be the joint probability density function of the values of the random variables ''f''₁ to ''f_n''. Then, the Chapman–Kolmogo ...