Symmetric Positive Semi-definate Covariance matrix using mvnrnd

I'm having an issue using mvnrnd. My covariance matrix is,

SIGMA = [12.96 14.076 0 0 0 0 0 0 0 0 0 0; 14.076 21.16 21.114 0 0 0 0 0 0 0 0 0; 0 21.114 29.16 27.54 0 0 0 0 0 0 0 0; 0 0 27.54 36 25.5 0 0 0 0 0 0 0; 0 0 0 25.5 25 17 0 0 0 0 0 0; 0 0 0 0 17 16 12.24 0 0 0 0 0; 0 0 0 0 0 12.24 12.96 9.792 0 0 0 0; 0 0 0 0 0 0 9.792 10.24 8.16 0 0 0; 0 0 0 0 0 0 0 8.16 9 8.415 0 0; 0 0 0 0 0 0 0 0 8.415 10.89 16.83 0; 0 0 0 0 0 0 0 0 0 16.83 36 28.05; 0 0 0 0 0 0 0 0 0 0 28.05 30.25]

All my eigenvalues are positive, and the matrix is symmetric, as far as I can tell, yet whenever I attempt to generate my RV's:

clear clc SIGMA = [12.96 14.076 0 0 0 0 0 0 0 0 0 0; 14.076 21.16 21.114 0 0 0 0 0 0 0 0 0; 0 21.114 29.16 27.54 0 0 0 0 0 0 0 0; 0 0 27.54 36 25.5 0 0 0 0 0 0 0; 0 0 0 25.5 25 17 0 0 0 0 0 0; 0 0 0 0 17 16 12.24 0 0 0 0 0; 0 0 0 0 0 12.24 12.96 9.792 0 0 0 0; 0 0 0 0 0 0 9.792 10.24 8.16 0 0 0; 0 0 0 0 0 0 0 8.16 9 8.415 0 0; 0 0 0 0 0 0 0 0 8.415 10.89 16.83 0; 0 0 0 0 0 0 0 0 0 16.83 36 28.05; 0 0 0 0 0 0 0 0 0 0 28.05 30.25] mu = [.9 2.3 5 12.5 8.8 -2 -4.3 -2.5 -1.5 .2 3.8 4.3] r = mvnrnd(mu, SIGMA, 2000)

I receive this error message.

??? Error using ==> mvnrnd at 118 SIGMA must be a symmetric positive semi-definite matrix.

Thanks for the help! David

Answer 1

[Matt J]

No, the eigenvalues of SIGMA are not positive. The EIG command reveals this immediately.

[David Young]

Thanks for your help!

If you saw my prev comment, I found the answer to my follow up question.

Answer 2

[Jurgen]

isequal(sum(eig(SIGMA)>0),length(eig(SIGMA)))

Why does eig(SIGMA) give negative eigenvalues?