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

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

References

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