Elementary linear algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Wiley
1973
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | Getr. Zählung graph. Darst. |
| ISBN: | 0471032476 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804122886111232000 |
|---|---|
| adam_text | Contents
Chapter 1
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 18
1.4 Matrices and Matrix Operations 22
1.5 Rules of Matrix Arithmetic 29
1.6 Inverses of Matrices 34
1.7 Elementary Matrices and a Method for Finding A 1 39
1.8 Further Results on Systems of Equations and Invertibility 47
Chapter 2 *
DETERMINANTS 55
2.1 The Determinant Function 55
2.2 Evaluating Determinants by Row Reduction 61
2.3 Properties of the Determinant Function 67
2.4 Cofactor Expansion; Cramer s Rule 74
Chapter 3
VECTORS IN 2 SPACE AND 3 SPACE 85
3.1 Introduction to Vectors (Geometric) 85
3.2 Norm of a Vector; Vector Arithmetic 95
3.3 Dot Product; Projections 98
3.4 Cross Product 105
3.5 Lines and Planes in 3 space 112
xi
xii | Contents
Chapter 4
VECTOR SPACES 121
4.1 Euclidean « Space 121
4.2 General Vector Spaces 126
4.3 Subspaces 131
4.4 Linear Independence 139
4.5 Basis and Dimension 145
4.6 Row Space of a Matrix; Coordinates; Applications to Finding Bases 152
4.7 Inner Product Spaces 160
4.8 Length and Angle in Inner Product Spaces 166
4.9 Orthonormal Bases; Gram Schmidt Process 172
Chapter 5
LINEAR TRANSFORMATIONS 183
5.1 Introduction to Linear Transformations 183
5.2 Properties of Linear Transformations: Kernel and Range 191
5.3 Matrix Transformations in Detail; Dimension Theorem 196
5.4 Matrices of Linear Transformations 205
5.5 Change of Basis 217
5.6 Similarity 228
Chapter 6
EIGENVALUES, EIGENVECTORS, AND QUADRATIC FORMS 233
6.1 Eigenvalues and Eigenvectors 233
6.2 Diagonalization 240
6.3 Orthogonal Diagonalization; Symmetric Matrices 246
6.4 Quadratic Forms; Conic Sections 252
6.5 Quadric Surfaces 263
Chapter 7
INTRODUCTION TO NUMERICAL METHODS OF
LINEAR ALGEBRA 271
7.1 Gaussian Elimination with Pivotal Condensation 271
7.2 The Gauss Seidel and Jacobi Methods 277
7.3 Approximating Eigenvalues by the Power Method 283
7.4 Approximating Nondominant Eigenvalues by Deflation 293
Answers to Exercises A.I
Index . ,
|
| any_adam_object | 1 |
| author | Anton, Howard 1939- |
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| callnumber-first | Q - Science |
| callnumber-label | QA251 |
| callnumber-raw | QA251 |
| callnumber-search | QA251 |
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| classification_rvk | SK 220 |
| ctrlnum | (OCoLC)347983 (DE-599)BVBBV008550948 |
| dewey-full | 512/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.5 |
| dewey-search | 512/.5 |
| dewey-sort | 3512 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| title | Elementary linear algebra |
| title_auth | Elementary linear algebra |
| title_exact_search | 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 | Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Lineare Algebra Aufgabensammlung Lehrbuch |
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