Linear Algebra: an introductory approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
[2000]
|
| Ausgabe: | [4. ed., reprint.] |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | X, 337 S. graph. Darst. |
| ISBN: | 9780387909929 |
Internformat
MARC
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| 264 | 1 | |a New York [u.a.] |b Springer |c [2000] | |
| 300 | |a X, 337 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804137753206587392 |
|---|---|
| adam_text | Contents
1.
Introduction
to Linear Algebra
1
1.
Some problems which lead to linear algebra
1
2.
Number systems and mathematical induction
6
2.
Vector Spaces and Systems of Linear Equations
16
3.
Vector spaces
16
4.
Subspaces and linear dependence
26
5.
The concepts of basis and dimension
34
6.
Row equivalence of matrices
38
7.
Some general theorems about finitely generated vector
spaces
48
8.
Systems of linear equations
53
9.
Systems of homogeneous equations
62
10.
Linear manifolds
69
3.
Linear Transformations and Matrices
75
1
1.
Linear transformations
75
12.
Addition and multiplication of matrices
88
13.
Linear transformations and matrices
99
4.
Vector Spaces with an Inner Product
109
14.
The concept of symmetry
109
15.
Inner products
119
ix
X
CONTENTS
5.
Determinants
132
16.
Definition of determinants
132
17.
Existence and uniqueness of determinants
140
18.
The multiplication theorem for determinants
146
19.
Further properties of determinants
150
6.
Polynomials and Complex Numbers
163
20.
Polynomials
163
21.
Complex numbers
176
7.
The Theory of a Single Linear Transformation
184
22.
Basic concepts
184
23.
Invariant subspaces
193
24.
The triangular form theorem
201
25.
The rational and Jordan canonical forms
216
8.
Dual Vector Spaces and Multilinear Algebra
228
26.
Quotient spaces and dual vector spaces
228
27.
Bilinear forms and duality
236
28.
Direct sums and tensor products
243
29.
A proof of the elementary divisor theorem
260
9.
Orthogonal and Unitary Transformations
266
30.
The structure of orthogonal transformations
266
31.
The principal axis theorem
271
32.
Unitary transformations and the spectral theorem
278
10.
Some Applications of Linear Algebra
289
33.
Finite symmetry groups in three dimensions
289
34.
Application to differential equations
298
35.
Analytic methods in matrix theory
306
36.
Sums of squares and Hurwitz s theorem
315
Bibliography (with Notes)
325
Solutions of Selected Exercises
327
Symbols (Including Greek Letters)
342
Index
344
|
| adam_txt |
Contents
1.
Introduction
to Linear Algebra
1
1.
Some problems which lead to linear algebra
1
2.
Number systems and mathematical induction
6
2.
Vector Spaces and Systems of Linear Equations
16
3.
Vector spaces
16
4.
Subspaces and linear dependence
26
5.
The concepts of basis and dimension
34
6.
Row equivalence of matrices
38
7.
Some general theorems about finitely generated vector
spaces
48
8.
Systems of linear equations
53
9.
Systems of homogeneous equations
62
10.
Linear manifolds
69
3.
Linear Transformations and Matrices
75
1
1.
Linear transformations
75
12.
Addition and multiplication of matrices
88
13.
Linear transformations and matrices
99
4.
Vector Spaces with an Inner Product
109
14.
The concept of symmetry
109
15.
Inner products
119
ix
X
CONTENTS
5.
Determinants
132
16.
Definition of determinants
132
17.
Existence and uniqueness of determinants
140
18.
The multiplication theorem for determinants
146
19.
Further properties of determinants
150
6.
Polynomials and Complex Numbers
163
20.
Polynomials
163
21.
Complex numbers
176
7.
The Theory of a Single Linear Transformation
184
22.
Basic concepts
184
23.
Invariant subspaces
193
24.
The triangular form theorem
201
25.
The rational and Jordan canonical forms
216
8.
Dual Vector Spaces and Multilinear Algebra
228
26.
Quotient spaces and dual vector spaces
228
27.
Bilinear forms and duality
236
28.
Direct sums and tensor products
243
29.
A proof of the elementary divisor theorem
260
9.
Orthogonal and Unitary Transformations
266
30.
The structure of orthogonal transformations
266
31.
The principal axis theorem
271
32.
Unitary transformations and the spectral theorem
278
10.
Some Applications of Linear Algebra
289
33.
Finite symmetry groups in three dimensions
289
34.
Application to differential equations
298
35.
Analytic methods in matrix theory
306
36.
Sums of squares and Hurwitz's theorem
315
Bibliography (with Notes)
325
Solutions of Selected Exercises
327
Symbols (Including Greek Letters)
342
Index
344 |
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| language | English |
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| spelling | Curtis, Charles W. 1926- Verfasser (DE-588)110295552 aut Linear Algebra an introductory approach [4. ed., reprint.] New York [u.a.] Springer [2000] X, 337 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Hier auch später erschienene, unveränderte Nachdrucke 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=016563762&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 |
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| title | Linear Algebra an introductory approach |
| title_auth | Linear Algebra an introductory approach |
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| title_full | Linear Algebra an introductory approach |
| title_fullStr | Linear Algebra an introductory approach |
| title_full_unstemmed | Linear Algebra an introductory approach |
| title_short | Linear Algebra |
| title_sort | linear algebra an introductory approach |
| title_sub | an introductory approach |
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| topic_facet | Lineare Algebra Einführung |
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