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The scrambling index of symmetric primitive matrices

โœ Scribed by Shexi Chen; Bolian Liu

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
328 KB
Volume
433
Category
Article
ISSN
0024-3795

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In [J.Y. Shao, L.H. You, Bound on the base of irreducible generalized sign pattern matrices, Discrete Math., in press], Shao and You extended the concept of the base from powerful sign pattern matrices to non-powerful (and generalized) sign pattern matrices. In this paper, we study the bases of prim

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The scrambling index of an n ร— n primitive matrix A is the smallest positive integer k such that A k (A t ) k = J, where A t denotes the transpose of A and J denotes the n ร— n all ones matrix. For an m ร— n Boolean matrix M, its Boolean rank b(M) is the smallest positive integer b such that M = AB fo

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The base sets of primitive zero-symmetric sign pattern matrices, Linear Algebra Appl. 428 (2008) [715][716][717][718][719][720][721][722][723][724][725][726][727][728][729][730][731] showed that the base set of quasi-primitive zerosymmetric (generalized) sign pattern matrices is {1, 2, . . . , 2n}.