Bounds on the bases of irreducible generalized sign pattern matrices
โ Scribed by Lihua You; Jiayu Shao; Haiying Shan
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 227 KB
- Volume
- 427
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
Any synthesis process based on a node-pair or mesh matrix must take cognizance of the sign pattern of the matrix. It is proved in general terms in this paper that: (1) the only subgraph of a connected graph G wbich need be of concern in studying the sign pattern of the node-pair (mesh) matrix is th
Let IBM(n, p) denote the set of all n ร n irreducible Boolean matrices with period p. This paper generalizes the concept of the index of maximum density of A, where A ~ IBM(n, p) with p > 1, and obtains upper bounds on the generalized maximum density index of IBM(n, p).
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
Let A be an n ร n nonnegative irreducible matrix, let A[ ] be the principal submatrix of A based on the nonempty ordered subset of {1, 2, . . . , n}, and define the generalized Perron complement of A[ ] by P t (A/A[ ]), i.e., This paper gives the upper and lower bounds on the Perron root of A. An u