%A Sookcharoenpinyo, Benchawan
%D 2018
%T A characterization of clean matrices in M3(Z)
%K clean matrix, idempotent matrix, Diophantine equation
%X An n x n matrix over a commutative ring with identity is clean if it is the sum of an idempotent matrix and a unit. In 2009, Rajeswari and Aziz gave necessary and sufficient criteria for a matrix in M 3 (Z) to be clean and discussed the involved Diophantine equations. In this paper, we extend those results to a larger set, M 3 (Z). We characterize when a matrix is clean. As its application, we discuss the relation between clean matrices and the existence of non-trivial solution of certain types of Diophantine equations.
%U http://www.journal.nu.ac.th/NUJST/article/view/1585
%J Naresuan University Journal: Science and Technology (NUJST)
%0 Journal Article
%P 72-77%V 26
%N 1
%@ 2539-553X
%8 2018-03-05