Matrix representation of a sixth order Sturm-Liouville problem and related inverse problem with finite spectrum

‎In this paper‎, ‎we find matrix representation of a class of sixth order Sturm-Liouville problem (SLP) with separated‎, ‎self-adjoint boundary conditions and we show that such SLP have finite spectrum‎. ‎Also for a given matrix eigenvalue problem $HX=\lambda VX$‎, ‎where $H$ is a block tridiagonal matrix and $V$ is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of Atkinson type that is equivalent to matrix eigenvalue problem.