mvnpdf says my covariance matrix is not symmetric and positive-definite. BUT IT IS!

The matrix I'm working with is

G=[1.193220936874846 1.752209119064988 0; 1.752209119064988 2.573066480861231 0; 0 0 2.666666666666666];

and the way that I test whether a matrix is positive-definite is

[R, err] = cholcov(G, 0).

If err is 0 then it is positive-definite, but if it's > 0 then the matrix is not positive-definite.

So, given that, Matlab says that G is positive-definite but that .5*G is not! According to the link below (#2 under further properties), any scalar multiple of a positive-definite matrix is also positive-definite.

So what gives? Anybody know a way to work around this and use my matrix .5*G as the sigma argument in mvnpdf?

http://en.wikipedia.org/wiki/Positive-definite_matrix#cite_note-HJobs713-3

Answer 1

[Walter Roberson]

That same page says that in order for a matrix to be positive definite, all of the eigenvalues must be positive.

>> eig(G)
ans =
                         0
          2.66666666666667
          3.76628741773608

0 is not positive, so G is not positive definite by that definition.

To understand what is going on...

>> cond(G)
ans =
      1.50674422424918e+16

That is above 1/eps so you are losing enough precision in doing the calculations as to render them suspect; different calculation routines might or might not explode for them.