Vol. 6, No. 1, 2013

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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
Abstract

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
Mathematical Subject Classification 2010
Primary: 15A18, 15B35
Milestones
Received: 4 August 2011
Revised: 25 April 2012
Accepted: 16 June 2012
Published: 23 June 2013

Communicated by Charles R. Johnson
Authors
D. D. Olesky
Department of Computer Science
University of Victoria
Victoria, British Columbia V8W 3P6
Canada
Michael F. Rempel
Department of Mathematics and Statistics
University of Victoria
Victoria, British Columbia V8W 3R4
Canada
P. van den Driessche
Department of Mathematics and Statistics
University of Victoria
Victoria, British Columbia V8W 3R4
Canada
www.math.uvic.ca/faculty/pvdd/