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Discussion: All Topics in Probability & Statistics
Topic: need help in generating feasible correlation matrices

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Subject:   feasible correlation matrices
Author: George
Date: Jan 22 2004
Huijing Chen
This, from Jerry Uhl,-George

In 5 dimensions, take 6 random vectors,
Appply Gram-Schmidt to get an orthonormal set X1,X2,...,X6.

Make a matrix H with Xi in the ith column.
Make a matrix A with Xi in the ith row.
Choose  nonneg numbers a1,a2, ...a6.

Make a diagonal matrix A with ai on the ith slot of the diagonal.

The matrix you want is H D A

On Jan 15, 2004, Huijing Chen wrote:

New Topic
Can anyone tell me how to generate feasible correlation matrices, i.e. real,
symmetric, positive semi-definite matrices?  Currently I generate a symmetric
matrix randomly, then use Householder tranformation to tridiagonalise the
matrix, then use QR algorithm to calculate eigenvalues.  If any of the
eigenvalue is negative, then the whole process is repeated until a positive
semi-definite matrix is found.  For a 5 by 5 matrix, it ran on my computer for
15 hours and didn't come up with a feasible matrix!  I suspect it is not a very
efficient way.  Can anyone tell me if there are any other algorithms or methods?

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