TY - JOUR

T1 - Geometric Parter–Wiener, etc. theory

AU - Johnson, Charles R.

AU - Saiago, Carlos M.

N1 - info:eu-repo/grantAgreement/FCT/5876/147204/PT#
sem pdf conforme despacho.

PY - 2018/1/15

Y1 - 2018/1/15

N2 - For real symmetric, or complex Hermitian, matrices whose graph is a tree, there is a well-developed (via several papers) theory about the possible multiplicities of the eigenvalues. It includes a theory of vertices whose removal increases a multiplicity (the “Parter–Wiener, etc. theory” and the “downer branch mechanism”), how to determine maximum multiplicity, lower bounds for the minimum number of distinct eigenvalues, etc. Remarkably, a great deal of this theory may be generalized to geometric multiplicities of general matrices over a field (with very different proofs). We show here what parts of this theory generalize, and, in the process, review the theory.

AB - For real symmetric, or complex Hermitian, matrices whose graph is a tree, there is a well-developed (via several papers) theory about the possible multiplicities of the eigenvalues. It includes a theory of vertices whose removal increases a multiplicity (the “Parter–Wiener, etc. theory” and the “downer branch mechanism”), how to determine maximum multiplicity, lower bounds for the minimum number of distinct eigenvalues, etc. Remarkably, a great deal of this theory may be generalized to geometric multiplicities of general matrices over a field (with very different proofs). We show here what parts of this theory generalize, and, in the process, review the theory.

KW - Eigenvalue

KW - General matrix

KW - Geometric multiplicity

KW - Maximum multiplicity

KW - Parter vertex

KW - Tree

UR - http://www.scopus.com/inward/record.url?scp=85031725197&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2017.09.035

DO - 10.1016/j.laa.2017.09.035

M3 - Article

AN - SCOPUS:85031725197

VL - 537

SP - 332

EP - 347

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -