ABSTRACT

Concepts from linear algebra play an important role in various applications of discrete mathematics, as in coding theory, computer graphics, marketing, generation of pseudorandom numbers, graph theory, and combinatorial designs. This chapter discusses fundamental concepts of linear algebra, computational aspects, and various applications. The concept of a "vector" comes initially from the physical world, where a vector is a quantity having both magnitude and direction. The mathematical concept of a vector space generalizes these ideas, with applications in coding theory, finite geometry, cryptography, and other areas of discrete mathematics. By imposing additional structure on real and complex vector spaces, the concepts of length, distance, and orthogonality can be introduced. These concepts are motivated by the corresponding geometric notions for physical vectors. Linear transformations are special types of functions that map one vector space to another.