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...

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...

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...

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...

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...

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

(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...

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

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...

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

{\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...

( 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 ⁡...

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...

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

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

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

respective random variables.: p.333  The covariance matrix (also called second central moment or variance-covariance matrix) of an n × 1 {\displaystyle n\times...

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...

three parameters: location parameter μ, covariance matrix Γ {\displaystyle \Gamma } , and the relation matrix C {\displaystyle C} . The standard complex...

covariance matrix of the samples. When the affine span of the samples is not the entire R N {\displaystyle \mathbb {R} ^{N}} , the covariance matrix would...

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...

{\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}...

theory and statistics, the covariance function describes how much two random variables change together (their covariance) with varying spatial or temporal...

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

}K\mathbf {g} >0\ ,} implying that the conductivity matrix should be positive definite. Covariance matrix M-matrix Positive-definite function Positive-definite...

\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...