On involutiveness of linear combinations of a quadratic matrix and an arbitrary matrix

Authors : Nurgül KALAYCI, Murat SARDUVAN

Pages : 1012-1027

Doi:10.15672/hujms.705784

View : 19 | Download : 4

Publication Date : 2021-08-06

Article Type : Research Paper

Abstract :We characterize the involutiveness of the linear combinations of the form $a{\mathbf{A}} + b{\mathbf{B}}$ when $a,b$ are nonzero complex numbers, ${\mathbf{A}}$ is a quadratic $n \times n$ nonzero matrix and ${\mathbf{B}}$ is an arbitrary $n \times n$ nonzero matrix, under certain properties imposed on $\mathbf{A}$ and $\mathbf{B}$.
Keywords : Quadratic matrix, Partitioned matrix, Linear combination, Diagonalization, Direct sum of matrices