Discrete Mathematical Structures

12

Vector Spaces

LEARNING OBJECTIVES

After reading this chapter, you will be conversant with:

• Introduction
• Definition
• Vector Subspace
• Calculus of Subspaces
• Linear Dependence and Indepence of Vectors
• Dimension and Basis
• Linear Transformation
• Normed and Inner Product Spaces

12.1 INTRODUCTION

Algebraic structures such as semigroups, monoids, rings, and fields provide a powerful tool in the theory as well as applications to computer science. Another algebraic structure essentially required for thorough understanding of graph theory-related problems and their solutions is the concept of Vector spaces.

12.2 DEFINITION

A vector space consists of the following:

1. A field (F, +,.) whose elements are called scalars.
2. A set V of objects called vectors on ...