Přihlásit se Vyzkoušet zdarma

Follow us

This website uses cookies

We use cookies to improve user experience. Choose which cookies you allow us to use. You can read more about our Cookie Policy in our privacy policy

See Cookies Details
Categories Corporate
Free Textbook

Linear Algebra I

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.
Download free PDF textbooks or read online. Less than 15% adverts
Byznys předplatné zdarma během prvních 30 dnů, pak $5.99/m
Description
Content

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
  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
Laisser un commentaire
About the Author

Kenneth Kuttler

Discover Author
Related Content