In this paper, we investigate a second order non-selfadjoint matrix Sturm-Liouville equation including a boundary condition that depends on quadratic eigenvalue parameter. Along with presenting a condition that ensures that this boundary value problem (BVP) has finitely many eigenvalues and spectral singularities with finite multiplicities, we have studied the point spectrum of this (BVP).

eigenvalues, spectral singularities, spectral analysis, Sturm-Liouville operator, non-selfadjoint matrix operator.