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

15 views (last 30 days)
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>>

Accepted Answer

Steven Lord
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."
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.
  1 Comment
Morten Nissov
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.

Sign in to comment.

More Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by