Introduction to linear algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
[2000]
|
| Edition: | 2. ed., [reprint.] |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 293 S. graph. Darst. |
| ISBN: | 9780387962054 0387962050 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to linear algebra |c Serge Lang |
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Record in the Search Index
| _version_ | 1804137922729869312 |
|---|---|
| adam_text | Contents
CHAPTER I
Vectors
......................................... 1
§1.
Definition of Points in Space
.......................... 1
§2.
Located Vectors
.................................. 9
§3.
Scalar Product
................................... 12
§4.
The Norm of a Vector
.............................. 15
§5.
Parametric Lines
.................................. 30
§6.
Planes
........................................ 34
CHAPTER
И
Matrices and Linear Equations
......................... 42
§1.
Matrices
....................................... 43
§2.
Multiplication of Matrices
............................ 47
§3.
Homogeneous Linear Equations and Elimination
.............. 64
§4.
Row Operations and Gauss Elimination
................... 70
§5
Row Operations and Elementary Matrices
.................. 77
§6.
Linear Combinations
............................... 85
CHAPTER III
Vector Spaces
..................................... 88
§1.
Definitions
...................................... 88
§2.
Linear Combinations
............................... 93
§3.
Convex Sets
..................................... 99
§4.
Linear Independence
............................... 104
§5.
Dimension
...................................... 110
§6.
The Rank of a Matrix
.............................. 115
Vlil
CONTENTS
CHAPTER TV
Linear Mappings
................................... 123
§1.
Mappings
...................................... 123
§2.
Linear Mappings
.................................. 127
§3.
The Kerne] and Image of a Linear Map
................... 136
§4.
The Rank and Linear Equations Again
.................... 144
§5.
The Matrix Associated with a Linear Map
.................. 150
Appendix: Change of Bases
............................. 154
CHAPTER V
Composition and Inverse Mappings
....................... 158
§1.
Composition of Linear Maps
.......................... 158
§2.
Inverses
....................................... 164
CHAPTER VI
Scalar Products and Orthogonality
....................... 171
§1.
Scalar Products
................................... 171
§2.
Orthogonal Bases
................................. 180
§3.
Bilinear Maps and Matrices
........................... 190
CHAPTER
VII
Determinants
..................................... 195
§1.
Determinants of Order
2............................. 195
§2. 3
χ
3
and
η χ
и
Determinants
......................... 200
§3.
The Rank of a Matrix and Subdeterminants
................. 210
§4.
Cramer s Rule
................................... 214
§5.
Inverse of a Matrix
................................ 217
§6.
Determinants as Area and Volume
....................... 221
CHAPTER
VIII
Eigenvectors and Eigenvalues
........................... 233
§1.
Eigenvectors and Eigenvalues
.......................... 233
§2.
The Characteristic Polynomial
......................... 238
§3.
Eigenvalues and Eigenvectors of Symmetric Matrices
........... 250
§4.
Diagonalization of a Symmetric Linear Map
................. 255
Appendix. Complex Numbers
............................ 260
Answers to Exercises
................................ 265
Index
........................................... 291
|
| adam_txt |
Contents
CHAPTER I
Vectors
. 1
§1.
Definition of Points in Space
. 1
§2.
Located Vectors
. 9
§3.
Scalar Product
. 12
§4.
The Norm of a Vector
. 15
§5.
Parametric Lines
. 30
§6.
Planes
. 34
CHAPTER
И
Matrices and Linear Equations
. 42
§1.
Matrices
. 43
§2.
Multiplication of Matrices
. 47
§3.
Homogeneous Linear Equations and Elimination
. 64
§4.
Row Operations and Gauss Elimination
. 70
§5
Row Operations and Elementary Matrices
. 77
§6.
Linear Combinations
. 85
CHAPTER III
Vector Spaces
. 88
§1.
Definitions
. 88
§2.
Linear Combinations
. 93
§3.
Convex Sets
. 99
§4.
Linear Independence
. 104
§5.
Dimension
. 110
§6.
The Rank of a Matrix
. 115
Vlil
CONTENTS
CHAPTER TV
Linear Mappings
. 123
§1.
Mappings
. 123
§2.
Linear Mappings
. 127
§3.
The Kerne] and Image of a Linear Map
. 136
§4.
The Rank and Linear Equations Again
. 144
§5.
The Matrix Associated with a Linear Map
. 150
Appendix: Change of Bases
. 154
CHAPTER V
Composition and Inverse Mappings
. 158
§1.
Composition of Linear Maps
. 158
§2.
Inverses
. 164
CHAPTER VI
Scalar Products and Orthogonality
. 171
§1.
Scalar Products
. 171
§2.
Orthogonal Bases
. 180
§3.
Bilinear Maps and Matrices
. 190
CHAPTER
VII
Determinants
. 195
§1.
Determinants of Order
2. 195
§2. 3
χ
3
and
η χ
и
Determinants
. 200
§3.
The Rank of a Matrix and Subdeterminants
. 210
§4.
Cramer's Rule
. 214
§5.
Inverse of a Matrix
. 217
§6.
Determinants as Area and Volume
. 221
CHAPTER
VIII
Eigenvectors and Eigenvalues
. 233
§1.
Eigenvectors and Eigenvalues
. 233
§2.
The Characteristic Polynomial
. 238
§3.
Eigenvalues and Eigenvectors of Symmetric Matrices
. 250
§4.
Diagonalization of a Symmetric Linear Map
. 255
Appendix. Complex Numbers
. 260
Answers to Exercises
. 265
Index
. 291 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed., [reprint.] |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T21:41:48Z |
| indexdate | 2024-07-09T21:20:00Z |
| institution | BVB |
| isbn | 9780387962054 0387962050 |
| language | English |
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| physical | VIII, 293 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Springer |
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| series2 | Undergraduate texts in mathematics |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Introduction to linear algebra Serge Lang 2. ed., [reprint.] New York [u.a.] Springer [2000] VIII, 293 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics 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 DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016674197&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 |
| spellingShingle | Lang, Serge 1927-2005 Introduction to linear algebra 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_exact_search_txtP | Introduction to linear algebra |
| title_full | Introduction to linear algebra Serge Lang |
| title_fullStr | Introduction to linear algebra Serge Lang |
| title_full_unstemmed | Introduction to linear algebra Serge Lang |
| title_short | Introduction to linear algebra |
| title_sort | introduction to linear algebra |
| topic | Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Lineare Algebra Einführung |
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