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 -