Abstract
We characterize the class CG(s) of matrices A for which the linear system Ax b can be solved by an s-term conjugate gradient method. We show that, except for a few anomalies, the class CG(s) consists of matrices A for which conjugate gradient methods are already known. These matrices are the Hermitian matrices, A*= A, and the matrices of the form A ei(dI + B), with B* =-B.
