Özdemir, HÖzban, AYMathematics2024-07-052024-07-052004320096-30031873-564910.1016/j.amc.2003.10.0272-s2.0-5644244491https://doi.org/10.1016/j.amc.2003.10.027https://hdl.handle.net/20.500.14411/1229Özdemir, Halim/0000-0003-4624-437XP-1, P-2 and P-3 being any three different nonzero mutually commutative n x n idempotent matrices, and C-1 C-2 and C-3 being nonzero scalars, the problem of characterizing some situations, where a linear combination of the form P = c(1)P(1) + c(2)P(2) or P = c(1)P(1) + c(2)P(2) + c(3)P(3), is also an idempotent matrix has been considered. Moreover two interesting results about the idempotency of linear combinations of 2 x 2 idempotent matrices and 3 x 3 idempotent matrices have been given. A statistical interpretation of the idempotency problem considered in this study has also been pointed out. (C) 2003 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccesssimilar matricesdiagonalizationidempotent matricesquadratic formsChi-square distributionArticleQ11592439448WOS:000224774100014