Minimal Critical Sets of Refined Inertias for Irreducible Sign Patterns of Order 2

Ber-Lin Yu

doi:10.4236/alamt.2013.32002

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Minimal Critical Sets of Refined Inertias for Irreducible Sign Patterns of Order 2

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DOI: 10.4236/alamt.2013.32002 2,367 Downloads 6,284 Views Citations

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Ber-Lin Yu

Affiliation(s)

Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an, China.

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.

KEYWORDS

Associated Digraph; Inertially Arbitrary Sign Pattern; Refined Inertia; Critical Set of Refined Inertias

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

B. Yu, "Minimal Critical Sets of Refined Inertias for Irreducible Sign Patterns of Order 2," Advances in Linear Algebra & Matrix Theory, Vol. 3 No. 2, 2013, pp. 7-10. doi: 10.4236/alamt.2013.32002.

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