Exercises of Vectors and Vectorial Spaces E-Book

Simone Malacrida

• Herausgeber: Simone Malacrida
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2022

Beschreibung

In this book, exercises are carried out regarding the following mathematical topics:
vectors and vector operations
vector spaces
canonical, orthogonal, and orthonormal bases.
Initial theoretical hints are also presented to make the performance of the exercises understood

Leseprobe

Table of Contents

“Exercises of Vectors and Vectorial Spaces”

INTRODUCTION

THEORETICAL OUTLINE

EXERCISES

“Exercises of Vectors and Vectorial Spaces”

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

vectors and vector operations

vector spaces

canonical, orthogonal, and orthonormal bases.

Initial theoretical hints are also presented to make the performance of the exercises understood

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – THEORETICAL OUTLINE

Vector definition

Carrier operations

Vector spaces

Operations on vector spaces

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II – EXERCISES

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 17

Exercise 18

Exercise 19

Exercise 20

Exercise 2 1

Exercise 22

Exercise 23

Exercise 24

Exercise 25

Exercise 26

INTRODUCTION

In this exercise book some examples of calculus related to vectors and vector spaces are carried out.

Furthermore, the main theorems used in this sector of geometry are presented.

Vectors allow us to generalize elementary geometry and lay the foundations for a more in-depth understanding of elements of abstract analysis.

The physical and technological applications of vectors are immeasurable, just think of any sector, starting from mechanics or electromagnetism.

In order to understand in more detail what is presented in the resolution of the exercises, the theoretical reference context is recalled in the first chapter.

What is presented in this workbook is generally addressed in university-level geometry courses, even if the notion of vector is already introduced in high school.

I

THEORETICAL OUTLINE

Vector definition

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A vector can be defined as an n-tuple of numbers where each individual number is called an element or component of the vector.

The vector symbol is a lowercase letter with an arrow above it:

A vector written in this way is called a row vector, a vector in which the elements are written vertically is called a column vector.

The number of elements of a vector is called the basis of the vector or vector basis .

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Carrier operations

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The sum and difference of vectors is the sum and difference of the individual elements of vectors .