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

Year 2021, Volume: 50 Issue: 4, 1012 - 1027, 06.08.2021

Nurgül Kalaycı , Murat Sarduvan

https://doi.org/10.15672/hujms.705784

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

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