a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving...

calculating covariance Analysis of covariance Autocovariance Covariance function Covariance matrix Covariance operator Distance covariance, or Brownian...

probability theory and statistics, 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...

variance-covariance matrix (or simply covariance matrix) showing also the relationship between each pair of variables. This would be a 3×3 matrix when 3...

Covariance matrix adaptation evolution strategy (CMA-ES) is a particular kind of strategy for numerical optimization. Evolution strategies (ES) are stochastic...

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

of the data's covariance matrix. Thus, the principal components are often computed by eigendecomposition of the data covariance matrix or singular value...

{\displaystyle 1\leq j\leq k} . The inverse of the covariance matrix is called the precision matrix, denoted by Q = Σ − 1 {\displaystyle {\boldsymbol {Q}}={\boldsymbol...

_{k}} is the covariance matrix of the observation noise, v k {\displaystyle \mathbf {v} _{k}} . Additionally, the cross covariance matrix is also needed...

matrix is required to be positive semi-definite (possibly non-symmetric) in order that entropy production be nonnegative. Covariance matrix M-matrix Positive-definite...

a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is...

referred to as the residual maker matrix or the annihilator matrix. The covariance matrix of the residuals r {\displaystyle \mathbf {r} } , by error propagation...

of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they are uncorrelated...

the value of x {\displaystyle x} . More generally, if the variance-covariance matrix of disturbance ε i {\displaystyle \varepsilon _{i}} across i {\displaystyle...

positive semi-definite square matrix, commonly referred to as the variance-covariance matrix (or simply as the covariance matrix). If X {\displaystyle X} is...

(e_{t}e_{t}')=\Omega \,} . The contemporaneous covariance matrix of error terms is a k × k positive-semidefinite matrix denoted Ω. E ( e t e t − k ′ ) = 0 {\displaystyle...

steps: a translation, the computation of a covariance matrix, and the computation of the optimal rotation matrix. Both sets of coordinates must be translated...

variable. Then the variances and covariances can be placed in a covariance matrix, in which the (i, j) element is the covariance between the i th random variable...

The covariance matrix (also called second central moment) K Z Z {\displaystyle \operatorname {K} _{\mathbf {Z} \mathbf {Z} }} contains the covariances between...

generalized least squares, when all the off-diagonal entries of the covariance matrix of the errors, are null. The fit of a model to a data point is measured...

of the autocorrelation matrix are real and non-negative. The auto-covariance matrix is related to the autocorrelation matrix as follows: K X X = E ⁡...

{\displaystyle d} is Gaussian multivariate-distributed with zero mean and unit covariance matrix N ( 0 p , I p , p ) {\displaystyle N(\mathbf {0} _{p},\mathbf {I}...

( ℜ ( Z ) , ℑ ( Z ) ) {\displaystyle (\Re {(Z)},\Im {(Z)})} has a covariance matrix of the form: [ Var ⁡ [ ℜ ( Z ) ] Cov ⁡ [ ℑ ( Z ) , ℜ ( Z ) ] Cov ⁡...

column vector μ {\displaystyle \mu } , and their variances and covariances in a covariance matrix Σ {\displaystyle \Sigma } . Consider a portfolio of risky...

used in statistics and econometrics to provide an estimate of the covariance matrix of the parameters of a regression-type model where the standard assumptions...

uncorrelated if and only if their cross-covariance matrix K X Y {\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {Y} }} matrix is zero. In the case of two complex...

Sample Matrix Inversion (SMI) uses the estimated (sample) interference covariance matrix in place of the actual interference covariance matrix. This is...

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

\end{aligned}}} The solution can be reformulated using elements of the covariance matrix: β ^ = s x , y s x 2 = r x y s y s x {\displaystyle {\widehat {\beta...

high-dimensional statistical phenomenon can be found in the problem of covariance matrix estimation. Suppose that we observe X 1 , … , X n ∈ R p {\displaystyle...