A note on the spectra of tridiagonal matrices

Using orthogonal polynomials, we give a different approach to some recent results on tridi-agonal matrices. 1. Introduction and preliminaries. Most of the results on tridiagonal matrices can be seen in the context of orthogonal polynomials. Here, we will see two examples. The aim of this note is to give simplified proofs of some recent results on tridiagonal matrices , using arguments from the theory of orthogonal polynomials. One of the most important tools in the study of orthogonal polynomials is the spectral theorem for orthogonal polynomials, which states that any orthogonal polynomial sequence (OPS) {P n } n≥0 is characterized by a three-term recurrence relation