Is there a relation between eigenvalues of a matrix and the eigenvalues of a differential operator in a Sturm-Liouville problem? The two problems are denoted by $AV=\lambda V$ and $Lf=\lambda f$ respectively. where $A$ is a matrix, $L$ is a differential second order operator, $V$ is eigenvector, $f$ is eigenfunction and $\lambda$ is eigenvalue. One can see what has transformed into what. If the two problems are related, is there a similar approach to matrix problem which can be used in Sturm-Liouville problem in order to derive the eigen-values?
The relation of eigenvalues in linear algebra and Sturm-Liouville problems
eigenvalues-eigenvectorssturm-liouville
Best Answer
Both problems are special cases of a vast general theory, known as spectral theory. This book of Davies comes to mind, but there are literally hundreds of book on this subject.