Integrally normalizable matrices with respect to a given set
| Autor: | Sudipta Mallik, Bryan L. Shader |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Numerical Analysis Algebra and Number Theory Spanning tree 010102 general mathematics Diagonal 010103 numerical & computational mathematics Characterization (mathematics) 01 natural sciences Combinatorics Set (abstract data type) Matrix (mathematics) Integrally closed Integer matrix Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | Linear Algebra and its Applications. 498:317-325 |
| ISSN: | 0024-3795 |
| Popis: | The n × n matrix A is integrally normalizable with respect to a prescribed subset M of { ( i , j ) : i , j = 1 , 2 , … , n and i ≠ j } provided A is diagonally similar to an integer matrix each of whose entries in positions corresponding to M is equal to 1. In the case that the elements of M form the arc set of a spanning tree, the matrices that are integrally normalizable with respect to M have been characterized. This paper gives a characterization for general subsets M. In addition, necessary and sufficient conditions for each matrix with a given zero–nonzero pattern to be integrally normalizable with respect to an arbitrary subset M are given. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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