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

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Morten Nissov on 29 Oct 2019
Commented: Morten Nissov on 20 Nov 2019
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>>

Steven Lord on 29 Oct 2019
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."
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 on 20 Nov 2019
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.