Covariance matrix
different from: Cross-covariance matrix
label: Kovarianzmatrix @de
label: Matrice delle covarianze @it
label: مصفوفة تغاير @ar
label: 分散共分散行列 @ja
label: Covariantiematrix @nl
label: Matriz de covarianza @es
label: 协方差矩阵 @zh
label: Matriz de covariância @pt
label: Ковариационная матрица @ru
label: Macierz kowariancji @pl
label: Kovarianční matice @cs
label: Matrice de variance-covariance @fr
label: Коваріаційна матриця @uk
label: Matriu de covariància @ca
urlname: CovarianceMatrix
subject: Category:Matrices
subject: Category:Covariance and correlation
subject: Category:Summary statistics
content: Indeed, from the property 4 it follows that under linear transformation of random variable with covariation matrix by linear operator s.a. , the covariation matrix is tranformed as : . As according to the property 3 matrix is symmetric, it can be diagonalized by a linear orthogonal transformation, i.e. there exists such orthogonal matrix , that : and are eigenvalues of . But this means that this matrix is a covariation matrix for a random variable , and the main diagonal of consists of variances of elements of vector. As variance is always non-negative, we conclude that for any . But this means that matrix is positive-semidefinite.
id: p/c026820
description: Verallgemeinerung der Varianz auf mehrdimensionale Zufallsvariablen @de
description: Objektu-multzo bati p aldagai behatuz gero, bi aldagaikako kobariantzek osatzen duten (p, p) matrizea. Matrizearen diagonalean, beraz, aldagaien beren buruarekiko sakabanatzeak adierazten duten bariantzak gertatzen dira. @eu
description: measure of covariance of components of a random vector
description: ベクトル要素間の共分散の行列 @ja
description: matice kovariancí náhodných veličin @cs
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