Numerotation functions for band and symmetric band matrices and the multiplicity calculation of a given eigenvalue λ for a tridiagonal matrix

Abstract

We give two numerotation functions Φ and Ψ respectively for a (real) band and symmetric band matrix, then we give an algorithm for the multiplicity calculation of a given eigenvalue λ for A ϵ $\text{R}$^{n × n} tridiagonal matrix.