On the spectra of some matrices derived from two quadratic matrices

Ozdemir, H.; Petik, T.

On the spectra of some matrices derived from two quadratic matrices

Document Type : Research Paper

Authors

H. Ozdemir ¹

T. Petik ²

¹ Department of Mathematics, University of Sakarya, TR54187, Sakarya, Turkey

² Department of Mathematics, University of Sakarya,TR54187, Sakarya, Turkey

Abstract

begin{abstract}
The relations between the spectrum of the matrix $Q+R$ and the spectra of the matrices
$(gamma + delta)Q+(alpha + beta)R-QR-RQ$, $QR-RQ$, $alpha beta R-QRQ$, $alpha RQR-(QR)^{2}$,
and $beta R-QR$ have been given on condition that the matrix $Q+R$ is diagonalizable, where $Q$,
$R$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $n$.
end{abstract}

Keywords

Quadratic matrix

idempotent matrix

spectrum

linear combination

diagonalization

Subjects