A Note on Decomposable and Reducible Integer Matrices

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URI: http://hdl.handle.net/10498/25643

DOI: 10.3390/sym13071125

ISSN: 2073-8994

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Author/s
Marijuán, Carlos; Ojeda, Ignacio; Vigneron Tenorio, AlbertoAuthority UCA
Date
2021-07
Department
Matemáticas
Source
Symmetry 2021, 13(7), 1125
Abstract
We propose necessary and sufficient conditions for an integer matrix to be decomposable in terms of its Hermite normal form. Specifically, to each integer matrix, we associate a symmetric integer matrix whose reducibility can be efficiently determined by elementary linear algebra techniques, and which completely determines the decomposability of the first one.
Subjects
integer matrix; hermite normal form; decomposable matrix; reducible matrix; disconnected graph
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This work is under a Creative Commons License Atribución 4.0 Internacional