On idempotency of linear combinations of a quadratic or a cubic matrix and an arbitrary matrix


Murat Sarduvan, Nurgül Kalaycı




Let A be a quadratic or a cubic n × n nonzero matrix and B be an arbitrary n × n nonzero matrix. In this study, we have established necessary and sufficient conditions for the idempotency of the linear combinations of the form aA + bB, under the some certain conditions imposed on A and B, where a, b are nonzero complex numbers,