Covariance matrix information

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...

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...

{\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...

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

_{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...

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

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...

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

( 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 ⁡...

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

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

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

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...

Pentland in face classification. The eigenvectors are derived from the covariance matrix of the probability distribution over the high-dimensional vector space...

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

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

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

conjugate prior of the inverse covariance-matrix of a multivariate-normal random-vector. Suppose G is a p × n matrix, each column of which is independently...

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...

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

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