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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:

Covariance matrix for two matrices:

Covariance between two vectors:

Covariance matrix for a matrix:

Out[1]//MatrixForm=

Covariance matrix for two matrices:

Out[1]//MatrixForm=

Covariances for machine-precision reals:

Use arbitrary precision:

Find the covariance between vectors of complexes:

Compute the covariance of a SparseArray:

Compute the covariance of two financial time series:

The covariance tends to be large only on the diagonal of a random matrix:

The covariance of a list with itself is the variance:

The diagonal of a covariance matrix is the variance:

A covariance matrix scaled by standard deviations is a correlation matrix:

Compute the covariance for a GCD array: