TY - JOUR
T1 - The inverse nullity pair problem and the strong nullity interlacing property
AU - Abiad, Aida
AU - Curtis, Bryan A.
AU - Flagg, Mary
AU - Hall, H. Tracy
AU - Lin, Jephian C.H.
AU - Shader, Bryan
PY - 2024/10/15
Y1 - 2024/10/15
N2 - The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph G. In this paper, we refer to the i-nullity pair of a matrix A as (null(A),null(A(i)), where A(i) is the matrix obtained from A by removing the i-th row and column. The inverse i-nullity pair problem is considered for complete graphs, cycles, and trees. The strong nullity interlacing property is introduced, and the corresponding supergraph lemma and decontraction lemma are developed as new tools for constructing matrices with a given nullity pair.
AB - The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph G. In this paper, we refer to the i-nullity pair of a matrix A as (null(A),null(A(i)), where A(i) is the matrix obtained from A by removing the i-th row and column. The inverse i-nullity pair problem is considered for complete graphs, cycles, and trees. The strong nullity interlacing property is introduced, and the corresponding supergraph lemma and decontraction lemma are developed as new tools for constructing matrices with a given nullity pair.
KW - Eigenvalue interlacing
KW - Inverse eigenvalue problem
KW - Rooted graph minor
KW - Strong Arnold property
KW - Strong nullity interlacing property
UR - http://www.scopus.com/inward/record.url?scp=85199697253&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2024.07.014
DO - 10.1016/j.laa.2024.07.014
M3 - Article
AN - SCOPUS:85199697253
SN - 0024-3795
VL - 699
SP - 539
EP - 568
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -