# AbsoluteCorrelation

AbsoluteCorrelation[v1,v2]

gives the absolute correlation between the vectors v1 and v2.

gives the absolute correlation matrix for the matrix m.

AbsoluteCorrelation[m1,m2]

gives the absolute correlation matrix for the matrices m1 and m2.

AbsoluteCorrelation[dist]

gives the absolute correlation matrix for the multivariate symbolic distribution dist.

AbsoluteCorrelation[dist,i,j]

gives the (i,j) absolute correlation for the multivariate symbolic distribution dist.

# Details • AbsoluteCorrelation[v1,v2] gives the unbiased estimate of the absolute correlation between v1 and v2.
• The lists v1 and v2 must be the same length.
• AbsoluteCorrelation[v1,v2] is equivalent to v1. Conjugate[v2]/Length[v1].
• For a matrix m with columns, is a × matrix of the absolute correlations between columns of m.
• For an × matrix m1 and an × matrix m2, AbsoluteCorrelation[m1,m2] is a × matrix of the absolute correlations between columns of m1 and columns of m2.
• AbsoluteCorrelation[dist,i,j] gives Expectation[xixj,{x1,x2,}dist].
• AbsoluteCorrelation[dist] gives an absolute correlation matrix with the (i,j) entry given by AbsoluteCorrelation[dist,i,j].

# Examples

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## Basic Examples(3)

Absolute correlation between two vectors:

 In:= Out= Absolute correlation matrix for a matrix:

 In:= Out//MatrixForm= Absolute correlation matrix for two matrices:

 In:= Out//MatrixForm= ## Neat Examples(1)

Introduced in 2012
(9.0)