Free Textbook

Linear Algebra I

Name: Linear Algebra I
Rating: 4.625 (24 reviews)
Author: Kenneth Kuttler

Matrices and Row operations

by Kenneth Kuttler

(24 ratings)

208

Language: English

This consists of the elementary aspects of linear algebra which depend mainly on row operations involving elementary manipulations of matrices.

home.book.signup_free.after

Стоимость подписки: бесплатно первые 30 дней, далее — $5.99/месяц

Описание

Содержание

This consists of the elementary aspects of linear algebra which depend mainly on row operations involving elementary manipulations of matrices. The field of scalars is typically the field of complex numbers.

Click here to download the additional book files using Firefox or any browser which supports mathml.

Preface

Preliminaries
1. Sets And Set Notation
2. Functions
3. The Number Line And Algebra Of The Real Numbers
4. Ordered fields
5. The Complex Numbers
6. The Fundamental Theorem Of Algebra
7. Exercises
8. Completeness of R
9. Well Ordering And Archimedean Property
10. Division
11. Systems Of Equations
12. Exercises
13. Fn
14. Algebra in Fn
15. Exercises
16. The Inner Product In Fn
17. What Is Linear Algebra?
18. Exercises
Linear Transformations
1. Matrices
2. Exercises
3. Linear Transformations
4. Some Geometrically Dened Linear Transformations
5. The Null Space Of A Linear Transformation
6. Subspaces And Spans
7. An Application To Matrices
8. Matrices And Calculus
9. Exercises
Determinants
1. Basic Techniques And Properties
2. Exercises
3. The Mathematical Theory Of Determinants
4. The Cayley Hamilton Theorem
5. Block Multiplication Of Matrices
6. Exercises
Row Operations
1. Elementary Matrices
2. The Rank Of A Matrix
3. The Row Reduced Echelon Form
4. Rank And Existence Of Solutions To Linear Systems
5. Fredholm Alternative
6. Exercises
Some Factorizations
1. LU Factorization
2. Finding An LU Factorization
3. Solving Linear Systems Using An LU Factorization
4. The PLU Factorization
5. Justification For The Multiplier Method
6. Existence For The PLU Factorization
7. The QR Factorization
8. Exercises
Spectral Theory
1. Eigenvalues And Eigenvectors Of A Matrix
2. Some Applications Of Eigenvalues And Eigenvectors
3. Exercises
4. Schur’s Theorem
5. Trace And Determinant
6. Quadratic Forms
7. Second Derivative Test
8. The Estimation Of Eigenvalues
9. Advanced Theorems
10. Exercises
11. Cauchy’s Interlacing Theorem for Eigenvalues

Написать отзыв

home.book.about_author

Kenneth Kuttler

home.book.discover_author

Follow us

Linear Algebra I

Matrices and Row operations