Elementary linear algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1987
|
| Ausgabe: | 5. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Getr. Zählung |
| ISBN: | 0471848190 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804135809933115392 |
|---|---|
| adam_text | ELEMENTARY
LINEAR ALGEBRA
FIFTHEDITION
HOWARD ^
Drexel University
JOHN WILEY amp; SONS
New York • Chichester • Brisbane * Toronto - Singapore
Contents
Chapter One
SYSTEMS OF LINEAR EQUATIONS AND MATRICES 1
1 1 Introduction to Systems of Linear Equations 1
1 2 Gaussian Elimination 8
1 3 Homogeneous Systems of Linear Equations 19
1 4 Matrices and Matrix Operations 23
1 5 Rules of Matrix Arithmetic 31
1 6 Elementary Matrices and a Method for Finding A ~1 43
1 7 Further Results on Systems of Equations and Invertibility 51
Chapter Two
DETERMINANTS 65
2 1 The Determinant Function 65
2 2 Evaluating Determinants by Row Reduction 72
2 3 Properties of the Determinant Function 78
2 4 Cofactor Expansion; Cramer s Rule 84
Chapter Three
VECTORS IN 2-SPACE AND 3-SPACE 99
3 1 Introduction to Vectors (Geometric) 99
3 2 Norm of a Vector; Vector Arithmetic 109
3 3 Dot Product; Projections 112
3 4 Cross Product 122
3 5 Lines and Planes in 3-space 130
xiii
xiv I Contents
Chapter Four
VECTOR SPACES 143
4 1 Euclidean n-Space 143
4 2 General Vector Spaces 150
4 3 Subspaces 155
4 4 Linear Independence 164
4 5 Basis and Dimension 171
4 6 Row and Column Space; Rank; Finding Bases 179
4 7 Inner Product Spaces 191
4 8 Length and Angle in Inner Product Spaces 198
4 9 Orthonormal Bases; Gram-Schmidt Process 209
4 10 Coordinates; Change of Basis 221
Chapter Five
LINEAR TRANSFORMATIONS 245
5 1 Introduction to Linear Transformations 245
5 2 Properties of Linear Transformations; Kernel and Range 254
5 3 Linear Transformations from R to Rm; Geometry of
Linear Transformations from R2 to R2 263
5 4 Matrices of Linear Transformations 280
5 5 Similarity 290
Chapter Six
EIGENVALUES, EIGENVECTORS 301
6 1 Eigenvalues and Eigenvectors 301
6 2 Diagonalization 309
6 3 Orthogonal Diagonalization; Symmetric Matrices 318
Chapter Seven
APPLICATIONS* 329
7 1 Application to Differential Equations 329
7 2 Application to Approximation Problems; Fourier Series 335
7 3 Quadratic Forms 342
7 4 Diagonalizing Quadratic Forms; Application to Conic
Sections 351
7 5 Application to Quadric Surfaces 364
* Additional applications to business, economics, and the physical and social sciences are available in
the supplement to this text, Applications of Linear Algebra or in the expanded version of this text, Elementary
Linear Algebra with Applications
Contents / xv
Chapter Eight
INTRODUCTION TO NUMERICAL METHODS
OF LINEAR ALGEBRA 371
8 1 Comparison of Procedures for Solving Linear Systems 371
82L [/-Decompositions 382
8 3 The Gauss-Seidel and Jacobi Methods 391
8 4 Partial Pivoting; Reduction of Roundoff Error 398
8 5 Approximating Eigenvalues by the Power Method 404
8 6 Approximating Nondominant Eigenvalues; Deflation and
Inverse Power Methods 413
Chapter Nine
COMPLEX VECTOR SPACES 421
9 1 Complex Numbers 421
9 2 Modulus; Complex Conjugate; Division 429
9 3 Polar Form; DeMoivre s Theorem 437
9 4 Complex Vector Spaces 447
9 5 Complex Inner Product Spaces 454
9 6 Unitary, Normal, and Hermitian Matrices 463
ANSWERS TO EXERCISES Al
INDEX II
|
| adam_txt |
ELEMENTARY
LINEAR ALGEBRA
FIFTHEDITION
HOWARD ^
Drexel University
JOHN WILEY amp; SONS
New York • Chichester • Brisbane * Toronto - Singapore
Contents
Chapter One
SYSTEMS OF LINEAR EQUATIONS AND MATRICES 1
1 1 Introduction to Systems of Linear Equations 1
1 2 Gaussian Elimination 8
1 3 Homogeneous Systems of Linear Equations 19
1 4 Matrices and Matrix Operations 23
1 5 Rules of Matrix Arithmetic 31
1 6 Elementary Matrices and a Method for Finding A ~1 43
1 7 Further Results on Systems of Equations and Invertibility 51
Chapter Two
DETERMINANTS 65
2 1 The Determinant Function 65
2 2 Evaluating Determinants by Row Reduction 72
2 3 Properties of the Determinant Function 78
2 4 Cofactor Expansion; Cramer's Rule 84
Chapter Three
VECTORS IN 2-SPACE AND 3-SPACE 99
3 1 Introduction to Vectors (Geometric) 99
3 2 Norm of a Vector; Vector Arithmetic 109
3 3 Dot Product; Projections 112
3 4 Cross Product 122
3 5 Lines and Planes in 3-space 130
xiii
xiv I Contents
Chapter Four
VECTOR SPACES 143
4 1 Euclidean n-Space 143
4 2 General Vector Spaces 150
4 3 Subspaces 155
4 4 Linear Independence 164
4 5 Basis and Dimension 171
4 6 Row and Column Space; Rank; Finding Bases 179
4 7 Inner Product Spaces 191
4 8 Length and Angle in Inner Product Spaces 198
4 9 Orthonormal Bases; Gram-Schmidt Process 209
4 10 Coordinates; Change of Basis 221
Chapter Five
LINEAR TRANSFORMATIONS 245
5 1 Introduction to Linear Transformations 245
5 2 Properties of Linear Transformations; Kernel and Range 254
5 3 Linear Transformations from R to Rm; Geometry of
Linear Transformations from R2 to R2 263
5 4 Matrices of Linear Transformations 280
5 5 Similarity 290
Chapter Six
EIGENVALUES, EIGENVECTORS 301
6 1 Eigenvalues and Eigenvectors 301
6 2 Diagonalization 309
6 3 Orthogonal Diagonalization; Symmetric Matrices 318
Chapter Seven
APPLICATIONS* 329
7 1 Application to Differential Equations 329
7 2 Application to Approximation Problems; Fourier Series 335
7 3 Quadratic Forms 342
7 4 Diagonalizing Quadratic Forms; Application to Conic
Sections 351
7 5 Application to Quadric Surfaces 364
* Additional applications to business, economics, and the physical and social sciences are available in
the supplement to this text, Applications of Linear Algebra or in the expanded version of this text, Elementary
Linear Algebra with Applications
Contents / xv
Chapter Eight
INTRODUCTION TO NUMERICAL METHODS
OF LINEAR ALGEBRA 371
8 1 Comparison of Procedures for Solving Linear Systems 371
82L [/-Decompositions 382
8 3 The Gauss-Seidel and Jacobi Methods 391
8 4 Partial Pivoting; Reduction of Roundoff Error 398
8 5 Approximating Eigenvalues by the Power Method 404
8 6 Approximating Nondominant Eigenvalues; Deflation and
Inverse Power Methods 413
Chapter Nine
COMPLEX VECTOR SPACES 421
9 1 Complex Numbers 421
9 2 Modulus; Complex Conjugate; Division 429
9 3 Polar Form; DeMoivre's Theorem 437
9 4 Complex Vector Spaces 447
9 5 Complex Inner Product Spaces 454
9 6 Unitary, Normal, and Hermitian Matrices 463
ANSWERS TO EXERCISES Al
INDEX II |
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| title | Elementary linear algebra |
| title_auth | Elementary linear algebra |
| title_exact_search | Elementary linear algebra |
| title_exact_search_txtP | Elementary linear algebra |
| title_full | Elementary linear algebra |
| title_fullStr | Elementary linear algebra |
| title_full_unstemmed | Elementary linear algebra |
| title_short | Elementary linear algebra |
| title_sort | elementary linear algebra |
| topic | Algèbre linéaire Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algèbre linéaire Algebras, Linear Lineare Algebra Aufgabensammlung Lehrbuch |
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