Non-self-adjoint Dirac Operator Eigenvalue's Trace Identity

About Dirac eigenvalue problem with general two points' liner algebra, corresponding operator of which often is non-self-adjoint operator. The asymptotic estimations of solution of initial value problem are obtained for Dirac equation by use of the transformation matrix operator in this thesis. Constructing an entire function a;(A), the zeros of which are the eigenvalue of Dirac eigenvalue problem with general two points' linear algebra boundary conditions. Through discussing every term's coefficient of a;(A), the general two points' linear algebra boundary conditions are turned into eight element typies, eight corresponding entire functions u(\) deciding eigenvalue and their asymptotic estimations on the corresponding circuits are gotten. By resorting to the integral identity and the residue method , asymptotic estimations of the Dirac operator eigenvalue are considered and eigenvalue's trace identities are obtained.