# The Application of Tridiagonal Matrices in P-polynomial Table Algebras

## TL;DR

This paper explores how tridiagonal matrices can be used to analyze characters of P-polynomial table algebras, revealing eigen-structures and recursive relations for their intersection matrices.

## Contribution

It introduces new methods for studying P-polynomial table algebras using tridiagonal matrices, including eigen-structure analysis and recursive formulas for characteristic polynomials.

## Key findings

- Eigen-structure results for special tridiagonal matrices
- Recursive relation for characteristic polynomial of intersection matrices
- Application of LU factorization in algebra analysis

## Abstract

In this paper, we study the characters of two classes of P-polynomial table algebras using tridiagonal matrices. To this end, we obtain some results about the eigen-structure of special tridiagonal matrices. We also find a recursive relation for the characteristic polynomial of the first intersection matrix of P-polynomial table algebras by means of LU factorization.