Spectral theory has been the most informative tool about physical and mathematical structures in the history of modern mathematics. With the mathematical publications in the last sixty years, this subject has shown a rapid development. Spectral analysis of differential equations with periodic coefficients arising in solid state physics and the theory of metals related to the quantum mechanics of crystals has been one of the common interests of physicists and mathematicians. The concept of spectral analysis here is actually the process of finding the eigenvalues formed by the equation under certain conditions and the solution functions called eigenfunctions obtained by placing these eigenvalues in the equation. Many problems from quantum physics such as vibration of a wire with two ends connected, electrostatic potential on a surface, heat conduction on a conductive rod to wave theory are expressed with different forms of linear differential equations. In this study, it is discussed how a linear differential equation arises as an eigenvalue problem for a differential operator in an infinite dimensional vector space. In addition, the concept of self-parity is defined by using the analogy with linear transformations in finite-dimensional space and it is shown how the properties of real eigenvalues and orthogonal eigenvectors of a self-equivalent matrix are translated into Theorem 3.