Abstract
We consider a nonsymmetric first order differential operator
where P is a 2 × 2 matrix whose compnents are of C1 class on [0,1]. We study an eigenvalue problem for A with boundary conditions at x=0,1. We establish an asympotic form of the eigenvalues and prove that the set of the root vectors forms a Riesz basis in {l2(0,1)}2. Next we apply the Riesz basis for showing the uniqueness in inverse eigenvalue problems for nonsymmetric systems. The key is the transformation formula.