Generalized quadraticity of linear combination of two generalized quadratic matrices

Abstract

It is investigated the necessary and sufficient conditions for the generalized quadraticity of a linear combination of any two generalized quadratic matrices. The main result obtained is, in a sense, a generalization of the main results given in [Uc M, ozdemir H, ozban AY. On the quadraticity of linear combinations of quadratic matrices. Linear Multilinear Algebra. 2015;63:1125-1137.] which contains many of the results in the literature related to idempotency or involutivity of the linear combinations of idempotent and/or involutive matrices, to the generalized quadratic matrices.