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Refined inertias
of tree sign patterns of orders 2 and 3
D. D. Olesky, Michael F. Rempel and P. van den Driessche
Vol. 6 (2013), No. 1, 1–12
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Abstract |
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Sign patterns are matrices with only the sign of each entry specified. The refined inertia of a matrix categorizes the eigenvalues as positive, negative, zero or nonzero imaginary, and the refined inertia of a sign pattern is the set of all refined inertias allowed by real matrices with that sign pattern. The complete sets of allowed refined inertias for all tree sign patterns of orders 2 and 3 (up to equivalence and negation) are determined. |
Keywords
sign pattern, inertia, refined inertia, allow problems,
characteristic equation, eigenvalues
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Mathematical Subject Classification 2010
Primary: 15A18, 15B35
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Milestones
Received: 4 August 2011
Revised: 25 April 2012
Accepted: 16 June 2012
Published: 23 June 2013
Communicated by Charles R. Johnson
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Authors |
| D. D. Olesky | |
| Department of Computer Science University of Victoria Victoria, British Columbia V8W 3P6 Canada |
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| Michael F. Rempel | |
| Department of Mathematics and
Statistics University of Victoria Victoria, British Columbia V8W 3R4 Canada |
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| P. van den Driessche | |
| Department of Mathematics and
Statistics University of Victoria Victoria, British Columbia V8W 3R4 Canada |
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| www.math.uvic.ca/faculty/pvdd/ | |
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