DSpace at VNU: Linear Algebra III: Advanced topics Linear Algebra II

LinearAlgebraII
SpectralTheoryandAbstractVectorSpaces
KennethKuttler

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Kenneth Kuttler

Linear Algebra II Spectral Theory and
Abstract Vector Spaces

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Linear Algebra II Spectral Theory and Abstract Vector Spaces
© 2012 Kenneth Kuttler & Ventus Publishing ApS
ISBN 978-87-403-0241-7

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Linear Algebra II Spectral Theory
and Abstract Vector Spaces

Contents

Contents
Preface

Part I

1

Preliminaries

Part I

1.1

Sets And Set Notation

Part I

1.2

Functions

Part I

1.3

he Number Line And Algebra Of he Real Numbers

Part I

1.4

Ordered ields

Part I

1.5

he Complex Numbers

Part I

1.6

Exercises

Part I

1.7

Completeness of R

Part I

1.8

Well Ordering And Archimedean Property

Part I

1.9

Division And Numbers

Part I

1.10

Systems Of Equations

Part I

1.11

Exercises

Part I

1.12

n

F

Part I
n

1.13

Algebra in F

1.14

Exercises

Part I
Part I

1.15

n

he Inner Product In F

Part I

1.16

What Is Linear Algebra?

Part I

1.17

Exercises

Part I

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Linear Algebra II Spectral Theory
and Abstract Vector Spaces

Contents

2

Matrices And Linear Transformations

Part I

2.1

Matrices

Part I

2.2

Exercises

Part I

2.3

Linear Transformations

Part I

2.4

Subspaces And Spans

Part I

2.5

An Application To Matrices

Part I

2.6

Matrices And Calculus

Part I

2.7

Exercises

Part I

3

Determinants

Part I

3.1

Basic Techniques And Properties

Part I

3.2

Exercises

Part I

3.3

he Mathematical heory Of Determinants

Part I

3.4

he Cayley Hamilton heorem

Part I

3.5

Block Multiplication Of Matrices

Part I

3.6

Exercises

Part I

4

Row Operations

Part I

4.1

Elementary Matrices

Part I

4.2

he Rank Of A Matrix

Part I

4.3

he Row Reduced Echelon Form

Part I

4.4

Rank And Existence Of Solutions To Linear Systems

Part I

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