Integrally Normalizable Matrices with Respect to a Given Set

Authors

Sudipta Mallik, Marshall UniversityFollow
Bryan L. Shader

Document Type

Article

Publication Date

6-2016

Abstract

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.

Comments

Copyright © 2015 Elsevier Inc. All rights reserved.

Recommended Citation

Mallik, S., & Shader, B. L. (2016). Integrally normalizable matrices with respect to a given set. Linear Algebra and its Applications, 498, 317-325.