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Description: |
Given an nxn matrix A, an eigenvalue λ of A and an index i (1\le i \le n) we say that i is downer (respectively neutral or Parter), if the multiplicity of λ in the matrix A(i) (obtained from A by deleting row and column i is smaller (resp equal or greater) than the multiplicity of λ in A. We will gave an equivalent formulation of an index being downer, neutral or Parter in terms of perturbation on the diagonal entry in position A of A. Of course every index must be downer for at least an eigenvalue; in fact, for an irreducible Hermitian matrix A every index must be downer for at least two (distinct) eigenvalues. If the graph of A is a tree we will characterize the trees vertices (indices) that can be downers for just two eigenvalues. We will also discuss the more general problem of characterizing for a given k the trees and vertices that can be downers for k eigenvalues.
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Date: |
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| Start Time: |
15:00 |
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Speaker: |
Antonio Leal Duarte (CMUC, Univ. Coimbra)
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Institution: |
CMUC-UC
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Place: |
Room 5.5 DMUC
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| Research Groups: |
-Algebra and Combinatorics
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See more:
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