This chapter introduces the top-down algorithm to compute the generalized eigenvectors. It reviews the fundamental concepts of linear algebra, including domain, range, transformation, and null spaces. This is followed by the introduction of linear systems, which covers linearization of non-linear systems. The chapter investigates a special type of matrix called Boolean matrices, and its usage in system modeling of graphs and discrete event control (DEC) of event-triggered discrete event systems. The matrix-based DEC has been widely used for modeling and analysis of complex interconnected discrete event systems with shared resources, routing decisions, and dynamic resource management. The chapter covers the common mathematical tool called the singular value decomposition (SVD), along with its properties and some practical applications to engineering systems. In general, the numerical algorithm for SVD of matrices is extremely efficient and stable as compared to that of eigenvalue decomposition.