TY - JOUR
AU - Sookcharoenpinyo, Benchawan
PY - 2018
TI - A characterization of clean matrices in M3(Z)
JF - Naresuan University Journal: Science and Technology (NUJST); Vol 26 No 1 (2561): January - March 2018
KW - clean matrix, idempotent matrix, Diophantine equation
N2 - 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.
UR - http://www.journal.nu.ac.th/NUJST/article/view/1585