On the spectra of some matrices derived from two generalized quadratic matrices

In the first chapter, it is given some brief information about the subject and scope of the study and it is emphasized the importance of the concept of the spectrum. Also, it is mentioned from some studies existing in the literature related to matrix classes discussed in the study. Some fundamental concepts and properties which will be used throughout the study are given in the second chapter. In the third chapter of the study, some relations between the spectrum of the matrix A+B and the spectra of some matrices derived from the matrices A and B are established under the assumptions that α≠β, γ≠δ, AB≠BA, and A+B is diagonalizable, where A and B are an {α, β} and {γ, δ}-quadratic matrix, respectively. In the next chapter, it is extended the problems discussed for quadratic matrices in the preceding chapter to a pair of generalized quadratic matrices under some particular conditions. Some applications on the characterizations of the linear combinations of special types of matrices of the results established which are related to the spectra in third and fourth chapters and some examples illustrating the results obtained are given in the fifth chapter. The last chapter consists of some discussions and suggestions related to the study.