Exact eigenvalue and eigenvector solutions of certain tridiagonal generalized eigenvalue problems
Hung‐Wen Chang, Sen-Eon Liu, Sin-Yuan Mu · 2014
It is known that certain tridiagonal matrices have exact eigenvalues and eigenvectors. There are sixteen documented tridiagonal matrix families, from the discretization of the one-dimensional Helmholtz equation that possess such properties. Extended members of these matrices share a same set of eigenvectors making them commutative with respective to matrix multiplication. We may therefore construct, in a fairly straightforward way, exact closed-form solutions of certain tridiagonal generalized matrix eigenvalue problems.