On Idempotency of Linear Combinations of Two 2×2 Idempotent Matrices
Özge Öztekin, Alisar ALHAMAD · Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi · 2021
Let A and B be 2 × 2 non-zero complex matrices. Let P be a linear combination of A and B in the form of P=c_1 A+c_2 B where c_1,c_2 are nonzero scalar numbers. An idempotent matrix is a matrix which, when multiplied by itself, yields itself. In this study, we established the entries of idempotent matrix B according to a given A idempotent matrix such that P is also be an idempotent matrix. In addition, the result was obtained that this determined P matrix is a singular matrix.