On the spectra of some matrices derived from two quadratic matrices

The relations between the spectrum of the matrix Q+RQ+R and the spectra of the matrices (gamma+delta)Q+(alpha+beta)R−QR−RQ(gamma+delta)Q+(alpha+beta)R−QR−RQ, QR−RQQR−RQ, alphabetaR−QRQalphabetaR−QRQ, alphaRQR−(QR)2alphaRQR−(QR)2, and betaR−QRbetaR−QR have been given on condition that the matrix Q+RQ+R is diagonalizable, where QQ, RR are alpha,betaalpha,beta-quadratic matrix and gamma,deltagamma,delta-quadratic matrix, respectively, of order n