The volume of the spatial region corresponding to n × n correlation matrices

Sean Eastman; Selwyn Hollis; Kawee Numpacharoen; Jared Schlieper

doi:10.4169/amer.math.monthly.123.9.909

The volume of the spatial region corresponding to n × n correlation matrices

Sean Eastman, Selwyn Hollis, Kawee Numpacharoen, Jared Schlieper

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A correlation matrix may be associated with a point in a hypercube of a certain dimension, each of whose coordinates has magnitude less than or equal to one. Using a spherical form of the Cholesky decomposition, we compute the volume of the subset of the hypercube corresponding to all valid correlation matrices of a given size. Doing so enables us to determine the probability that a randomly chosen point in the hypercube corresponds to a valid correlation matrix.

Original language	English
Pages (from-to)	909-918
Number of pages	10
Journal	American Mathematical Monthly
Volume	123
Issue number	9
DOIs	https://doi.org/10.4169/amer.math.monthly.123.9.909
State	Published - 2016

Scopus Subject Areas

General Mathematics

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10.4169/amer.math.monthly.123.9.909

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AB - A correlation matrix may be associated with a point in a hypercube of a certain dimension, each of whose coordinates has magnitude less than or equal to one. Using a spherical form of the Cholesky decomposition, we compute the volume of the subset of the hypercube corresponding to all valid correlation matrices of a given size. Doing so enables us to determine the probability that a randomly chosen point in the hypercube corresponds to a valid correlation matrix.

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The volume of the spatial region corresponding to n × n correlation matrices

Abstract

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