factor_analyzer.factor_analyzer_utils.duplication_matrix

factor_analyzer.factor_analyzer_utils.duplication_matrix(n=1)

Calculate the duplication matrix.

A function to create the duplication matrix (Dn), which is the unique n2 × n(n+1)/2 matrix which, for any n × n symmetric matrix A, transforms vech(A) into vec(A), as in Dn vech(A) = vec(A).

Parameters

Name Type Description Default
n int The dimension of the n x n symmetric matrix. Defaults to 1. 1

Returns

Name Type Description
duplication_matrix :obj:numpy.ndarray The duplication matrix.

Raises

Name Type Description
ValueError If n is not a positive integer greater than 1.

References

https://en.wikipedia.org/wiki/Duplication_and_elimination_matrices