covariance matrix

Input interpretation

covariance matrix

Definition

Given n sets of variates denoted {X_1}, ..., {X_n} , the first-order covariance matrix is defined by V_(i j) = cov(x_i, x_j) congruent 〈(x_i - μ_i)(x_j - μ_j)〉, where μ_i is the mean. Higher order matrices are given by V_(i j)^(m n) = 〈(x_i - μ_i)^m (x_j - μ_j)^n〉. An individual matrix element V_(i j) = cov(x_i, x_j) is called the covariance of x_i and x_j.
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Related terms

covariance | error propagation | statistical correlation | variance

Subject classifications

MathWorld

matrix types

MSC 2010

15-XX
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