\R^n as a Vector Space

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Chapter 2 $\R^n$ as a Vector Space

In this chapter, we define $\R^n\text{,}$ the $n$-dimensional Euclidean space as vector space over $\R\text{.}$ We shall define abstract vector spaces in later chapter. In fact, $\R^n$ can be thought of as model vector spaces and once we understand properties in $\R^n\text{,}$ it will be easier to under properties in asbtract vector spaces. Sage is a very nice tool to define vector spaces and deal with all the concepts of vector space. We shall explore all the concepts in this chapter using Sage in the last section.

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Linear Algebra with SageMath: A Gentle Introduction

Chapter 2 \(\R^n\) as a Vector Space