Kovarianzmatrix
Matrice delle covarianze
مصفوفة تغاير
分散共分散行列
Covariantiematrix
Matriz de covarianza
协方差矩阵
Covariance matrix
Matriz de covariância
Ковариационная матрица
Macierz kowariancji
Kovarianční matice
Matrice de variance-covariance
Коваріаційна матриця
Matriu de covariància
CovarianceMatrix
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.
Verallgemeinerung der Varianz auf mehrdimensionale Zufallsvariablen
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.
measure of covariance of components of a random vector
ベクトル要素間の共分散の行列
matice kovariancí náhodných veličin
September 2024
An inverse concentration gets smaller the more concentrated something is, not larger as it reasonably should be. Besides, we already call it "concentration matrix" later on in this sentence, which is kind of contradictory.
Proof
Covariance Matrix