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...

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

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...

{\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...

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

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...

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

(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...

( 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 ⁡...

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

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

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...

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

Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component...

Gaussian) a covariance matrix C M {\displaystyle C_{M}} representing the a priori uncertainties on the model parameters, and a covariance matrix C D {\displaystyle...

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

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

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

by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates...

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...

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...

{\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}...

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...