Involutiveness of linear combinations of a quadratic‎ ‎or tripotent matrix and an arbitrary matrix

Abstract

In this article, we characterize the involutiveness of the linear combination of the form<br />a1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,<br />and A2 is arbitrary, under certain properties imposed on A1 and A2.