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

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 Subject: RE: feasible correlation matrices Author: rabeldin Date: Jan 7 2005
You can run an orthogonalization procedure backwards.

1) Start with a diagonal matrix S(0), that is positive semi-definite (or
definite if you desire). This will have your eigenvalues on the diagonal and
zeroes elsewhere.

2) Choose 2 coordinates at random. Call them i and j.

3) Generate a random angle A, between 0 and 2pi radians.

4) Construct the orthogonal matrix Q from an identity by replacing Q[i,j] with
sin(A), Q[j,i] with sin(-A), Q[i,i] with cos(A), and Q[j,j] with
cos(-A).

5) Construct S(k+1) from Q'S(k)Q.

6) Repeat steps 2 thru 5 as desired.

7) Reduce the resulting covariance matrix to a correlation matrix in the
ordinary way.

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