chol() say matrix is not positive defnite even though all eigenvalues are positive

Title exaplins it more or less. I need to make the cholesky decomposition of a matrix and the function, chol(), returns an error saying that the matrix is not positive definite.

The code in question:

Qd = [
    0.0106,    0.0178;
    0.0097,    0.0195
];
chol(Qd)

The Qd matrix is calcualted with through some more complex means but this is one example of a Qd matrix that returns the following outputs:

K>> Qd
Qd =
    0.0106    0.0178
    0.0097    0.0195
K>> chol(Qd)
Error using chol
Matrix must be positive definite. 
K>> eig(Qd)
ans =
    0.0011
    0.0289
K>> 

Answer 1

[Steven Lord]

You're not factorizing the matrix you think you're factorizing. From the documentation for the chol function: "If A is nonsymmetric , then chol treats the matrix as symmetric and uses only the diagonal and upper triangle of A."

Is your Qd matrix symmetric?

issymmetric(Qd) % false

So what matrix are you actually trying to factorize?

A = triu(Qd) + triu(Qd, 1).'

That matrix is symmetric but is not positive definite.

[Morten Nissov]

I completely forgot to check and had just assumed the matrix was symmetric. Thank you, this pointed me towards an underlying problem earlier in the script.