Ber-Lin Yu and Ting-Zhu Huang
A Note on the Minimum Cardinality of Critical Sets of Inertias for Irreducible Zerononzero Patterns of Order 4
142 - 144
2010
4
1
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10461
https://publications.waset.org/vol/37
World Academy of Science, Engineering and Technology
If there exists a nonempty, proper subset S of the set of all (n1)(n2)2 inertias such that S &Ocirc;&egrave;&aring; i(A) is sufficient for any n&times;n zerononzero pattern A to be inertially arbitrary, then S is called a critical set of inertias for zerononzero 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 Kim, Olesky and Driessche, Critical sets of inertias for matrix patterns, Linear and Multilinear Algebra, 57 (3) (2009) 293306, identifying all minimal critical sets of inertias for n&times;n zerononzero patterns with n &ge; 3 and the minimum cardinality of such a set are posed as two open questions by Kim, Olesky and Driessche. In this note, the minimum cardinality of all critical sets of inertias for 4 &times; 4 irreducible zerononzero patterns is identified.
Open Science Index 37, 2010