Document Type
Article
Journal/Book Title/Conference
Mathematics
Volume
7
Issue
1
Publisher
MDPI
Publication Date
1-9-2019
First Page
1
Last Page
6
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Abstract
Let S be an antinegative semiring. The rank of an m×n matrix B over S is the minimal integer r such that B is a product of an m×r matrix and an r×n matrix. The isolation number of B is the maximal number of nonzero entries in the matrix such that no two entries are in the same column, in the same row, and in a submatrix of B of the form [bi,j bk,j
bi,l bk,l] with nonzero entries. We know that the isolation number of B is not greater than the rank of it. Thus, we investigate the upper bound of the rank of B and the rank of its support for the given matrix B with isolation number h over antinegative semirings.
Recommended Citation
Beasley, L.B.; Song, S.-Z. Upper Bounds for the Isolation Number of a Matrix over Semirings. Mathematics 2019, 7, 65.
