Built-in Mathematica Symbol

Covariance

Covariance[v₁, v₂]
gives the covariance between lists v₁ and v₂.

Covariance[m]
gives the covariance matrix for the matrix m.

Covariance[m₁, m₂]
gives the covariance matrix for the matrices m₁ and m₂.

Covariance[v₁, v₂] gives the unbiased estimate of the covariance between v₁ and v₂.

Covariance[v₁, v₂] is equivalent to (v₁-Mean[v₁]). Conjugate[v₂-Mean[v₂]]/(Length[v₁]-1).

For a matrix m with p columns Covariance[m] is a p×p matrix of the covariances between columns of m.

For an n×p matrix m₁ and an n×q matrix m₂, Covariance[m₁, m₂] is a p×q matrix of the covariances between columns of m₁ and columns of m₂.

Covariance between two vectors:

Covariance matrix for a matrix:

Out[1]//MatrixForm=

Covariance matrix for two matrices:

Out[1]//MatrixForm=