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The book deals mainly with analyzing and characterizing certain classes of matrices, nonnegative matrices and generalizations of M-matrices. In particular, two types of generalized M-matrices, namely the class of GM -matrices and M_v-matrices are considered. More specifically, this involves a detailed study of the structure of the generalized eigenspace of nonnegative matrices and the generalized nullspace of generalized M-matrices. We attempt to generalize the combinatorial properties of singular M-matrices to the class of singular GM-matrices and singular M_v-matrices. Concepts of eventually monotonicity and eventually nonnegativity on subsets of R^n are introduced to characterize a subclass of M_v-matrices.