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variance covariance matrix |
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Cross-references: variance, iid, identically distributed, independent, symmetric, matrix, diagonals, random vector
There are 10 references to this entry.
This is version 5 of covariance matrix, born on 2004-06-30, modified 2007-05-09.
Object id is 5975, canonical name is CovarianceMatrix.
Accessed 25101 times total.
Classification:
| AMS MSC: | 62H99 (Statistics :: Multivariate analysis :: Miscellaneous) |
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Pending Errata and Addenda
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![$ Cov(X_i,X_i)=Var[X_i]$](http://images.planetmath.org:8080/cache/objects/5975/l2h/img6.png "$ Cov(X_i,X_i)=Var[X_i]$"){kind=small}
![$\displaystyle \mathbf{Cov(X)}=\begin{pmatrix}Var[X_1] & \cdots & Cov(X_1,X_n) \ \vdots & & \vdots \\ Cov(X_n,X_1) & \cdots & Var[X_n] \end{pmatrix}.$](http://images.planetmath.org:8080/cache/objects/5975/l2h/img7.png "$\displaystyle \mathbf{Cov(X)}=\begin{pmatrix}Var[X_1] & \cdots & Cov(X_1,X_n) \ \vdots & & \vdots \\ Cov(X_n,X_1) & \cdots & Var[X_n] \end{pmatrix}.$")
![$ \mathbf{Cov(X)}=\mathbf{Var[X]}$](http://images.planetmath.org:8080/cache/objects/5975/l2h/img8.png "$ \mathbf{Cov(X)}=\mathbf{Var[X]}$"){kind=small}
![$\displaystyle \begin{pmatrix}E[{X_1}^2]-E[X_1]^2 & \cdots & E[X_1X_n]-E[X_1]E[X... ...[X_n]^2 \end{pmatrix} = \mathbf{E\Big[\big(X-E[X]\big)\big(X-E[X]\big)^T\Big]}.$](http://images.planetmath.org:8080/cache/objects/5975/l2h/img9.png "$\displaystyle \begin{pmatrix}E[{X_1}^2]-E[X_1]^2 & \cdots & E[X_1X_n]-E[X_1]E[X... ...[X_n]^2 \end{pmatrix} = \mathbf{E\Big[\big(X-E[X]\big)\big(X-E[X]\big)^T\Big]}.$")
