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Abstract
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Sign pattern matrices of order
that allow inertias in the set
are considered. All sign patterns of order 3 (up to equivalence) that allow
are classified and organized according to their associated directed graphs.
Furthermore, a minimal set of such matrices is found. Then, given a pattern of order
that
allows
, a
construction is given that generates families of irreducible sign patterns of
order that
allow .
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Keywords
sign pattern, zero-nonzero pattern, inertia, digraph,
Jacobian
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Mathematical Subject Classification 2010
Primary: 15B35, 15A18, 05C50
Secondary: 05C20
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Milestones
Received: 29 January 2019
Revised: 8 June 2019
Accepted: 22 June 2019
Published: 12 October 2019
Communicated by Chi-Kwong Li
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