# Does conjugate gradient converge for negative definite matrices?

Guys I was reading about CG method to solve the sparse systems. I came across that the method is defined for positive definite symmetric matrices. I was wondering does it converges for negative definite matrices too ?

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Not directly, CG minimizes a convex quadratic. However, you could solve $(-A)x = (-b)$, or modify the algorithm by changing signs at appropriate places (as in the difference between minimization and maximization is 'just' a sign difference). –  copper.hat Nov 16 '12 at 4:13

$Ax =b \iff (-A) x = -b$, and if $A$ is symmetric negative definite then $-A$ is symmetric positive definite. So you can use CG to solve $-Ax = -b$.