Linear Algebra, 2nd Edition

Table of contents

1. Cover
2. Copyright
3. Contents
4. Preface
5. Preface to the Second Edition
6. A Note to Students
7. List of Symbols
8. Matrices
   1. 1.1INTRODUCTION
   2. 1.2BASIC CONCEPTS
   3. 1.3 MATRIX OPERATIONS AND THEIR PROPERTIES (1/3)
   4. 1.3 MATRIX OPERATIONS AND THEIR PROPERTIES (2/3)
   5. 1.3 MATRIX OPERATIONS AND THEIR PROPERTIES (3/3)
   6. 1.4 INVERTIBLE MATRICES
   7. 1.5 TRANSPOSE OF A MATRIX
   8. 1.6 PARTITION OF MATRICES; BLOCK MULTIPLICATION (1/2)
   9. 1.6 PARTITION OF MATRICES; BLOCK MULTIPLICATION (2/2)
   10. 1.7 GROUPS AND FIELDS
9. Systems of LinearEquations
   1. 2.1 INTRODUCTION
   2. 2.2 GAUSSIAN ELIMINATION
   3. 2.3 ELEMENTARY ROW OPERATIONS (1/2)
   4. 2.3 ELEMENTARY ROW OPERATIONS (2/2)
   5. 2.4 ROW REDUCTION (1/3)
   6. 2.4 ROW REDUCTION (2/3)
   7. 2.4 ROW REDUCTION (3/3)
   8. 2.5 INVERTIBLE MATRICES AGAIN
   9. 2.6 LU FACTORIZATION (1/3)
   10. 2.6 LU FACTORIZATION (2/3)
   11. 2.6 LU FACTORIZATION (3/3)
   12. 2.7 DETERMINANT (1/4)
   13. 2.7 DETERMINANT (2/4)
   14. 2.7 DETERMINANT (3/4)
   15. 2.7 DETERMINANT (4/4)
10. Vector Spaces
    1. 3.1 INTRODUCTION
    2. 3.2 BASIC CONCEPTS (1/3)
    3. 3.2 BASIC CONCEPTS (2/3)
    4. 3.2 BASIC CONCEPTS (3/3)
    5. 3.3 LINEAR INDEPENDENCE (1/2)
    6. 3.3 LINEAR INDEPENDENCE (2/2)
    7. 3.4 BASIS AND DIMENSION (1/3)
    8. 3.4 BASIS AND DIMENSION (2/3)
    9. 3.4 BASIS AND DIMENSION (3/3)
    10. 3.5 SUBSPACES AGAIN
    11. 3.6 RANK OF A MATRIX
    12. 3.7 ORTHOGONALITY IN Rn (1/3)
    13. 3.7 ORTHOGONALITY IN Rn (2/3)
    14. 3.7 ORTHOGONALITY IN Rn (3/3)
    15. 3.8 BASES OF SUBSPACES (1/2)
    16. 3.8 BASES OF SUBSPACES (2/2)
    17. 3.9 QUOTIENT SPACE (1/2)
    18. 3.9 QUOTIENT SPACE (2/2)
11. Linear Mapsand Matrices
    1. 4.1 INTRODUCTION
    2. 4.2 BASIC CONCEPTS
    3. 4.3 ALGEBRA OF LINEAR MAPS (1/3)
    4. 4.3 ALGEBRA OF LINEAR MAPS (2/3)
    5. 4.3 ALGEBRA OF LINEAR MAPS (3/3)
    6. 4.4 ISOMORPHISM (1/2)
    7. 4.4 ISOMORPHISM (2/2)
    8. 4.5 MATRICES OF LINEAR MAPS (1/4)
    9. 4.5 MATRICES OF LINEAR MAPS (2/4)
    10. 4.5 MATRICES OF LINEAR MAPS (3/4)
    11. 4.5 MATRICES OF LINEAR MAPS (4/4)
12. Linear Operators
    1. 5.1 INTRODUCTION
    2. 5.2 POLYNOMIALS OVER FIELDS
    3. 5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES (1/6)
    4. 5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES (2/6)
    5. 5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES (3/6)
    6. 5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES (4/6)
    7. 5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES (5/6)
    8. 5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES (6/6)
    9. 5.4 MINIMAL POLYNOMIAL (1/3)
    10. 5.4 MINIMAL POLYNOMIAL (2/3)
    11. 5.4 MINIMAL POLYNOMIAL (3/3)
    12. 5.5 INVARIANT SUBSPACES (1/3)
    13. 5.5 INVARIANT SUBSPACES (2/3)
    14. 5.5 INVARIANT SUBSPACES (3/3)
    15. 5.6 SOME BASIC RESULTS (1/3)
    16. 5.6 SOME BASIC RESULTS (2/3)
    17. 5.6 SOME BASIC RESULTS (3/3)
    18. 5.7 REAL QUADRATIC FORMS (1/3)
    19. 5.7 REAL QUADRATIC FORMS (2/3)
    20. 5.7 REAL QUADRATIC FORMS (3/3)
13. Canonical Forms
    1. 6.1 INTRODUCTION
    2. 6.2 PRIMARY DECOMPOSITION THEOREM
    3. 6.3 JORDAN FORMS (1/4)
    4. 6.3 JORDAN FORMS (2/4)
    5. 6.3 JORDAN FORMS (3/4)
    6. 6.3 JORDAN FORMS (4/4)
14. Bilinear Forms
    1. 7.1 INTRODUCTION
    2. 7.2 BASIC CONCEPTS
    3. 7.3 LINEAR FUNCTIONALS AND DUAL SPACE
    4. 7.4 SYMMETRIC BILINEAR FORMS (1/3)
    5. 7.4 SYMMETRIC BILINEAR FORMS (2/3)
    6. 7.4 SYMMETRIC BILINEAR FORMS (3/3)
    7. 7.5 GROUPS PRESERVING BILINEAR FORMS (1/2)
    8. 7.5 GROUPS PRESERVING BILINEAR FORMS (2/2)
15. Inner Product Spaces
    1. 8.1 INTRODUCTION
    2. 8.2 HERMITIAN FORMS
    3. 8.3 INNER PRODUCT SPACE
    4. 8.4 GRAM–SCHMIDT ORTHOGONALIZATION PROCESS (1/3)
    5. 8.4 GRAM–SCHMIDT ORTHOGONALIZATION PROCESS (2/3)
    6. 8.4 GRAM–SCHMIDT ORTHOGONALIZATION PROCESS (3/3)
    7. 8.5 ADJOINTS (1/2)
    8. 8.5 ADJOINTS (2/2)
    9. 8.6 UNITARY AND ORTHOGONAL OPERATORS (1/2)
    10. 8.6 UNITARY AND ORTHOGONAL OPERATORS (2/2)
    11. 8.7 NORMAL OPERATORS (1/3)
    12. 8.7 NORMAL OPERATORS (2/3)
    13. 8.7 NORMAL OPERATORS (3/3)
16. Bibliography
17. Index
18. Blank Page