The inertia set of nonnegative symmetric sign pattern with zero diagonal

Gao, Yubin, and Shao, Yan Ling. "The inertia set of nonnegative symmetric sign pattern with zero diagonal." Czechoslovak Mathematical Journal 53.4 (2003): 925-934. <http://eudml.org/doc/30825>.

@article{Gao2003,
abstract = {The inertia set of a symmetric sign pattern $A$ is the set $i(A)=\lbrace i(B) \mid B=B^T \in Q(A)\rbrace $, where $i(B)$ denotes the inertia of real symmetric matrix $B$, and $Q(A)$ denotes the sign pattern class of $A$. In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern $A$ in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns $A$ with zero diagonal that require unique inertia.},
author = {Gao, Yubin, Shao, Yan Ling},
journal = {Czechoslovak Mathematical Journal},
keywords = {sign pattern; inertia; inertia set; unique inertia; sign pattern; inertia; inertia set; unique inertia},
language = {eng},
number = {4},
pages = {925-934},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The inertia set of nonnegative symmetric sign pattern with zero diagonal},
url = {http://eudml.org/doc/30825},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Gao, Yubin
AU - Shao, Yan Ling
TI - The inertia set of nonnegative symmetric sign pattern with zero diagonal
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 925
EP - 934
AB - The inertia set of a symmetric sign pattern $A$ is the set $i(A)=\lbrace i(B) \mid B=B^T \in Q(A)\rbrace $, where $i(B)$ denotes the inertia of real symmetric matrix $B$, and $Q(A)$ denotes the sign pattern class of $A$. In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern $A$ in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns $A$ with zero diagonal that require unique inertia.
LA - eng
KW - sign pattern; inertia; inertia set; unique inertia; sign pattern; inertia; inertia set; unique inertia
UR - http://eudml.org/doc/30825
ER -