### Cholesky Decomposition

Posted:

**Mon Jan 30, 2006 9:24 pm**I will be working with real, symmetric matrices and need to determine if the matrices are positive definite—that’s all. Don’t have to solve the matrix, invert it, calculate its determinant, or anything else at the moment—just determine if it is positive definite. I have done a little investigation, for example, reading on the Mathworld site, which states, “A linear system of equations with a positive definite matrix can be efficiently solved using the so-called Cholesky decomposition.”

Okay . . .

(I am not a mathematics Ph.D., so please be patient with me.)

Two questions:

1) I went on the LAPACK site and tried to find a “Cholesky Decomposition“ using the LAPACK Search Engine. Looked in the “Computational Routines” section, in the “Orthogonal Factorization” and “Symmetric Eigenproblems” sub-sections. I did not find it. Either I am using the wrong terminology, or I am lost. Somebody please let me know what search terms to use. Alternately, if you happen to know exactly which routine to use, please let me know (for real, symmetric matrices).

2) Assuming I find a routine that does the decomposition, is that it? If the decomposition is possible, does that mean the matrix is positive definite, whereas if the routine fails, the matrix is not? Or are additional steps required?

Thanks for any help.

David

Okay . . .

(I am not a mathematics Ph.D., so please be patient with me.)

Two questions:

1) I went on the LAPACK site and tried to find a “Cholesky Decomposition“ using the LAPACK Search Engine. Looked in the “Computational Routines” section, in the “Orthogonal Factorization” and “Symmetric Eigenproblems” sub-sections. I did not find it. Either I am using the wrong terminology, or I am lost. Somebody please let me know what search terms to use. Alternately, if you happen to know exactly which routine to use, please let me know (for real, symmetric matrices).

2) Assuming I find a routine that does the decomposition, is that it? If the decomposition is possible, does that mean the matrix is positive definite, whereas if the routine fails, the matrix is not? Or are additional steps required?

Thanks for any help.

David