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@article{(International Science Index):http://waset.org/publications/11586, title = {Minimal Critical Sets of Inertias for Irreducible Zero-nonzero Patterns of Order 3}, author = {Ber-Lin Yu and Ting-Zhu Huang}, country = {}, institution={}, abstract = {If there exists a nonempty, proper subset S of the set of all (n + 1)(n + 2)/2 inertias such that S Ôèå i(A) is sufficient for any n × n zero-nonzero pattern A to be inertially arbitrary, then S is called a critical set of inertias for zero-nonzero patterns of order n. If no proper subset of S is a critical set, then S is called a minimal critical set of inertias. In [3], Kim, Olesky and Driessche identified all minimal critical sets of inertias for 2 × 2 zero-nonzero patterns. Identifying all minimal critical sets of inertias for n × n zero-nonzero patterns with n ≥ 3 is posed as an open question in [3]. In this paper, all minimal critical sets of inertias for 3 × 3 zero-nonzero patterns are identified. It is shown that the sets (0, 0, 3), (3, 0, 0), (0, 0, 3), (0, 3, 0), (0, 0, 3), (0, 1, 2), (0, 0, 3), (1, 0, 2), (0, 0, 3), (2, 0, 1) and (0, 0, 3), (0, 2, 1) are the only minimal critical sets of inertias for 3 × 3 irreducible zerononzero patterns. }, journal = {International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering}, volume = {4}, number = {1}, year = {2010}, pages = {127 - 129}, ee = {http://waset.org/publications/11586}, url = {http://waset.org/Publications?p=37}, bibsource = {http://waset.org/Publications}, issn = {eISSN:1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {International Science Index 37, 2010}, }