A Remark on Perfect Gaussian Elimination of Symmetric Matrices

AbstractLet M be a symmetric matrix with non-zero diagonal entries. A result of Golumbic [3, 5] states that if M has a perfect elimination scheme then it also has a perfect elimination scheme with the additional property that all pivots are chosen along the main diagonal. However, the proof given by Golumbic seems to be incomplete. In the present note, we refine Golumbic's proof, thus obtaining a complete version of it