TITLE:
Minimal Critical Sets of Refined Inertias for Irreducible Sign Patterns of Order 2
AUTHORS:
Ber-Lin Yu
KEYWORDS:
Associated Digraph; Inertially Arbitrary Sign Pattern; Refined Inertia; Critical Set of Refined Inertias
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.3 No.2,
June
14,
2013
ABSTRACT: Let S be a nonempty, proper
subset of all refined inertias. Then, S is called a critical
set of refined inertias for ireducible sign patterns of order n if is sufficient for any
sign pattern A to be refined inertially
arbitrary. If no proper subset of Sis a critical set of
refined inertias, then S is a minimal critical
set of refined inertias for sign patterns of order n . In this paper, all minimal critical sets of refined
inertias for irreducible sign patterns of order 2 are identified. As a
by-product, a new approach is presented to identify all minimal critical sets
of inertias for irreducible sign patterns of order 2.