Introduction to linear algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Macmillan
1972
|
| Edition: | 1. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 321 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to linear algebra |
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| 300 | |a XIV, 321 S. | ||
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| 650 | 4 | |a Algèbre linéaire | |
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Record in the Search Index
| _version_ | 1804117094710640640 |
|---|---|
| adam_text | CONTENTS
CHAPTER 1
Linear Equations 1
1.1 Linear Equations 1
1.2 Three Examples 2
1.3 Exercises 6
1.4 Equivalent Systems of Equations 9
1.5 The Echelon Form for Systems of Equations 12
1.6 Synthetic Elimination 14
1.7 Systems of Homogeneous Linear Equations 17
1.8 Exercises 19
1.9 Number Fields 21
1.10 Exercises 23
chapter 2
Matrices 25
2.1 Matrices 25
2.2 Equality of Matrices 26
2.3 Addition of Matrices 27
2.4 The Commutative and Associative Laws of Addition for 27
Matrices
2.5 Zero, Negatives, and Subtraction of Matrices 29
2.6 Scalar Multiples of Matrices 30
ix
x Contents
2.7 Multiplication of Matrices by Matrices 31
2.8 Properties of Matrix Multiplication 35
2.9 Exercises 39
2.10 Diagonal, Scalar, and Identity Matrices 44
2.11 The Inverse of a Matrix 45
2.12 The Transpose of a Matrix 50
2.13 Symmetric, Skew Symmetric, and Hermitian Matrices 51
2.14 Polynomial Functions of Matrices 52
2.15 Exercises 54
2.16 Partitioning of Matrices 57
2.17 Exercises 60
chapter 3
Vector Geometry in S2 and £z 63
3.1 Geometric Representations of Vectors 63
3.2 Operations on Vectors 65
3.3 Isomorphism 68
3.4 Length and Angle 68
3.5 Exercises 73
3.6 Lines in Space 74
3.7 Orthogonality of Vectors 76
3.8 The Angle Between Two Lines 79
3.9 The Equation of a Plane 80
3.10 Linear Combinations of Vectors in Sz 86
3.11 Linear Dependence of Vectors; Bases 89
3.12 Half Spaces in «?3 92
3.13 Exercises 97
chapter 4
Vector Geometry in // Dimensional Space 103
4.1 The Real « Space Mn 103
4.2 Vectors in 3tn 104
4.3 Lines and Planes in 0tn 105
4.4 Linear Dependence and Independence in 3 n 108
Contents xi
4.5 Vector Spaces in 0tn 109
4.6 Exercises 109
4.7 Length and the Cauchy Schwarz Inequality 111
4.8 Angles and Orthogonality in «fn 114
4.9 Half Lines and Directed Distances 116
4.10 Half Spaces 117
4.11 Unitary w Space 118
4.12 Exercises 120
chapter 5
Vector Spaces 125
5.1 The General Definition of a Vector Space 125
5.2 Linear Combinations and Linear Dependence 128
5.3 Exercises 133
5.4 Basic Theorems on Linear Dependence 136
5.5 Dimension and Basis 138
5.6 Computation of the Dimension of a Vector Space 143
5.7 Exercises 145
5.8 Orthonormal Bases 148
5.9 Exercises 150
5.10 Intersection and Sum of Two Vector Spaces 152
5.11 Exercises 154
5.12 Isomorphic Vector Spaces 155
5.13 The General Concept of a Field 158
5.14 Exercises 159
chapter 6
The Rank of a Matrix 161
6.1 The Rank of a Matrix 161
6.2 Basic Theorems About the Rank of a Matrix 164
6.3 Matrix Representation of Elementary Transformations 167
6.4 Exercises 171
6.5 Homogeneous Systems of Linear Equations 174
6.6 Nonhomogeneous Systems of Linear Equations 177
xii Contents
6.7 Exercises 181
6.8 The Variables One Can Solve For 184
6.9 Basic Solutions 186
6.10 Exercises 188
CHAPTER 7
Determinants 189
7.1 The Definition of a Determinant 189
7.2 Some Basic Theorems 192
7.3 The Cofactor in det A of an Element of A 196
7.4 Cofactors and the Computation of Determinants 199
7.5 Exercises 202
7.6 The Determinant of the Product of Two Matrices 204
7.7 A Formula for A 1 206
7.8 Determinants and the Rank of a Matrix 207
7.9 Solution of Systems of Equations by Using Determinants 209
7.10 A Geometrical Application of Determinants 212
7.11 Exercises 213
CHAPTER 8
Linear Transformations 219
8.1 Mappings 219
8.2 Linear Mappings 222
8.3 Some Properties of Linear Operators on Vector Spaces 224
8.4 Exercises 226
8.5 Some Geometrical Properties of Linear Transformations 228
8.6 Invariants of Transformations 232
8.7 Orthogonal Matrices and Orthogonal Transformations 235
8.8 Exercises 237
8.9 Orthogonal Vector Spaces 238
8.10 Exercises 241
8.11 Linear Transformations of Coordinates 242
8.12 Transformation of a Linear Operator 247
8.13 The Algebra of Linear Operators 249
8.14 Exercises 250
Contents xiii
CHAPTER 9
The Characteristic Value Problem 253
9.1 Definition of the Characteristic Value Problem 253
9.2 Two Examples 255
9.3 Two Basic Theorems 257
9.4 Exercises 259
9.5 Minor Determinants of a Matrix 261
9.6 The Characteristic Polynomial and Its Roots 261
9.7 Similar Matrices 265
9.8 Exercises 267
9.9 The Characteristic Roots of a Real Symmetric Matrix 267
9.10 The Diagonal Form of a Real Symmetric Matrix 269
9.11 The Diagonalization of a Real Symmetric Matrix 271
9.12 Characteristic Roots of a Polynomial Function of a Matrix 274
9.13 Exercises 277
9.14 Quadratic Forms 279
9.15 Diagonalization of Quadratic Forms 281
9.16 Definite Forms and Matrices 282
9.17 A Geometrical Application 286
9.18 Bilinear Forms 289
9.19 Exercises 292
APPENDIX I
The Notations 2 and n 295
1.1 Definitions 295
1.2 Exercises 297
1.3 Basic Rules of Operations 298
1.4 Exercises 300
1.5 Finite Double Sums 300
1.6 Exercises 302
1.7 Definitions and Basic Properties 304
1.8 Exercises 305
APPENDIX II
The Algebra of Complex Numbers 307
II. 1 Definitions and Fundamental Operations 307
II.2 Exercises 310
xjv Contents
11.3 Conjugation Complex Numbers 311
11.4 Exercises 313
Index 315
|
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| 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 |
| edition | 1. print. |
| format | Book |
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| spelling | Hohn, Franz E. Verfasser aut Introduction to linear algebra 1. print. New York u.a. Macmillan 1972 XIV, 321 S. txt rdacontent n rdamedia nc rdacarrier Algèbre linéaire Einführung swd Lineare Algebra swd Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Lineare Algebra (DE-588)4035811-2 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001753034&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hohn, Franz E. Introduction to linear algebra Algèbre linéaire Einführung swd Lineare Algebra swd Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4151278-9 |
| title | Introduction to linear algebra |
| title_auth | Introduction to linear algebra |
| title_exact_search | Introduction to linear algebra |
| title_full | Introduction to linear algebra |
| title_fullStr | Introduction to linear algebra |
| title_full_unstemmed | Introduction to linear algebra |
| title_short | Introduction to linear algebra |
| title_sort | introduction to linear algebra |
| topic | Algèbre linéaire Einführung swd Lineare Algebra swd Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algèbre linéaire Einführung Lineare Algebra Algebras, Linear |
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