Advances in Linear Algebra & Matrix Theory
Volume 3, Issue 2 (June 2013)
ISSN Print: 2165-333X ISSN Online: 2165-3348
Google-based Impact Factor: 0.11 Citations
Minimal Critical Sets of Refined Inertias for Irreducible Sign Patterns of Order 2 ()
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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.
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