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.