On the quadraticity of linear combinations of quadratic matrices
Mahmut Uç, Halim Özdemır, Ahmet Yaşar Özban · Linear and Multilinear Algebra · 2014
Let and be nonzero quadratic matrices and let and be nonzero complex numbers. Necessary and sufficient conditions for the quadraticity of the linear combinations of the form are obtained. Our main results contain many of the results in the literature related to idempotency or involutivity of the linear combinations of idempotent and/or involutive matrices. Finally, some numerical examples are given to exemplify the main results.