January 2014
Intermediate to advanced
576 pages
12h 56m
English
Content preview from Discrete Mathematical StructuresBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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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:
- A field (F, +,.) whose elements are called scalars.
- A set V of objects called vectors on ...
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