Introduction to Vectors, Matrices and Tensors E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

The theoretical assumptions of the following mathematical topics are presented in this book: vectors and vector calculus matrices and matrix calculus vector and matrix spaces mathematics and tensor calculus

Leseprobe

Simone Malacrida

Introduction to Vectors, Matrices and Tensors

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

“Introduction to Vectors, Matrices and Tensors”

INTRODUCTION

VECTORS AND VECTOR CALCULATION

MATRICES AND MATRIX CALCULATION

VECTOR SPACES

TENSORIAL MATHEMATICS

“Introduction to Vectors, Matrices and Tensors”

“Introduction to Vectors, Matrices and Tensors”

SIMONE MALACRIDA

The theoretical assumptions of the following mathematical topics are presented in this book:

vectors and vector calculus

matrices and matrix calculus

vector and matrix spaces

mathematics and tensor calculus

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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 – VECTORS AND VECTOR CALCULATION

Definitions

Operations

Applications

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II – MATRICES AND MATRIX CALCULATION

Definitions

Operations and properties

Matrix calculation

Applications

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III - VECTOR SPACES

Definitions

Operations on vector spaces

Matrix operations

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IV - TENSORIAL MATHEMATICS

Definitions

Operations

Particular tensors

INTRODUCTION

INTRODUCTION

In this book all aspects of vector, matrix and tensor mathematics are exposed.

Vectors find ample space in contemporary applications, from physics to economics.

For this reason, the first chapter presents the basic concepts of these entities with the related operations.

Identically, matrices play a fundamental role in science and technology and knowledge of their properties is a key factor in every aspect of contemporary society.

The first two chapters present both aspects just mentioned and, for their understanding, university knowledge is not necessary.

Conversely, the other two chapters need in-depth support from mathematical analysis, functional analysis and differential geometry.

Vector spaces are the most appropriate setting for both vectors and matrices which can be considered as completely different mathematical objects in this connotation.

The study of vector spaces and their properties generalizes and extends what was done in the first chapters of the manual.

Finally, a separate chapter is dedicated to tensor mathematics, precisely because of the considerable importance of these entities in the physical and technological world.

I

VECTORS AND VECTOR CALCULATION

VECTORS AND VECTOR CALCULATION

Definitions

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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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Operations

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

The sum between vectors is associative, commutative and has the neutral element given by the null vector .

Furthermore, each element has its opposite.