The change in eigenvalue multiplicity associated with perturbation of a diagonal entry

Abstract

We investigate the relation between perturbing the i-th diagonal entry of A ∈ ℳ _n (𝔽) and extracting the principal submatrix A(i) from A with respect to the possible changes in multiplicity of a given eigenvalue. A complete description is given and used to both generalize and improve prior work about Hermitian matrices whose graph is a given tree.

Keywords:

• eigenvalue multiplicity
• submatrices
• Hermitian matrices
• graph

AMS Subject Classifications::

• 15A18
• 15B57

Notes

This work was done within the activities of Centro de Matemática e Aplicações da Universidade Nova de Lisboa.

Additional information

Notes on contributors

Carlos M. Saiago

This work was done within the activities of Centro de Matemática e Aplicações da Universidade Nova de Lisboa.