Geometric linear algebra:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and indexes |
Internformat
MARC
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and indexes | ||
| 650 | 4 | |a Algebras, Linear |v Textbooks | |
| 650 | 4 | |a Geometry, Algebraic |v Textbooks | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-013101051 | ||
Datensatz im Suchindex
| _version_ | 1804133256493268992 |
|---|---|
| adam_text | CONTENTS
Preface
......................................
vii
Volume One
Part
1:
The Affine and Linear
Structures of
M1, M2 and
R3
1
Chapter
1
The One-Dimensional Real Vector Space
R
(or R1)
....... 5
Introduction
................................... 5
Sketch of the Content
.............................. 7
1.1
Vectorization of a Straight Line:
Affine
Structure
............ 7
1.2
Coordinatization of a Straight Line: R1 (or R)
.............. 10
1.3
Changes of Coordinates:
Affine
and Linear Transformations
(or Mappings)
................................ 14
1.4
Affine
Invariants
............................... 17
Chapter
2
The Two-Dimensional Real Vector Space K2
........... 21
Introduction
................................... 21
Sketch of the Content
.............................. 23
2.1
(Plane) Vector
................................ 24
2.2
Vectorization of a Plane:
Affine
Structure
................. 30
2.3
Coordinatization of a Plane: R2
...................... 34
2.4
Changes of Coordinates:
Affine
and Linear Transformations
(or Mappings)
................................ 45
2.5
Straight Lines in a Plane
.......................... 59
2.6
Affine
and Barycentric Coordinates
.................... 70
2.7
Linear Transformations (Operators)
.................... 81
2.7.1
Linear operators in the Cartesian coordinate system
....... 86
2.7.2
Examples
............................... 91
2.7.3
Matrix representations of a linear operator in various bases
... 114
2.2.4
Linear transformations (operators)
................. 135
2.7.5
Elementary matrices and matrix factorizations
.......... 148
2.7.6
Diagonal canonical form
....................... 186
2.2.7
Jordan canonical form
........................ 218
2.7.8
Rational canonical form
....................... 230
ххп
Contents
2.8 Affine
Transformations
...........................235
2.8.1 Matrix
representations
........................239
2.8.2
Examples
...............................250
2.8.3 Affine
invariants
...........................285
2.8.4 Affine
geometry
............................292
2.8.5
Quadratic curves
...........................300
Chapter
3
The Three-Dimensional Real Vector Space R3
.......... 319
Introduction
................................... 319
Sketch of the Content
.............................. 321
3.1
Vectorization of a Space:
Affine
Structure
................ 322
3.2
Coordinatization of a Space: R3
...................... 326
3.3
Changes of Coordinates:
Affine
Transformation (or Mapping)
..... 335
3.4
Lines in Space
................................ 345
3.5
Planes in Space
............................... 350
3.6 Affine
and Barycentric Coordinates
.................... 361
3.7
Linear Transformations (Operators)
.................... 365
3.7.1
Linear operators in the Cartesian coordinate system
....... 365
3.7.2
Examples
............................... 384
3.7.3
Matrix representations of a linear operator in various bases
. . . 406
3.7.4
Linear transformations (operators)
................. 435
3.7.5
Elementary matrices and matrix factorizations
.......... 442
3.7.6
Diagonal canonical form
....................... 476
37.7
Jordan canonical form
........................ 511
3.7.8
Rational canonical form
....................... 558
3.8 Affine
Transformations
........................... 578
3.8.1
Matrix representations
........................579
3.8.2
Examples
...............................590
3.8.3 Affine
invariants
...........................636
3.8.4 Affine
geometry
............................640
3.8.5
Quadrics
................................668
Appendix A Some Prerequisites
........................681
A.I Sets
......................................681
A.2 Functions
..................................682
A.3 Fields
.....................................684
A.
4
Groups
....................................686
A.
5
Polynomials
.................................687
Appendix
В
Fundamentals of Algebraic Linear Algebra
...........691
B.I Vector (or Linear) Spaces
..........................691
B.2 Main Techniques: Linear Combination, Dependence and Independence
695
B.3 Basis and Dimension
............................697
B.4 Matrices
...................................699
Contents xxiii
В.
5
Elementary Matrix Operations and Row-Reduced Echelon Matrices
. 719
B.6 Determinants
............................... 727
B.7 Linear Transformations and Their Matrix Representations
...... 732
B.8 A Matrix and its Transpose
....................... 756
B.9 Inner Product Spaces
........................... 773
B.10 Eigenvalues and Eigenvectors
...................... 790
B.ll Diagonalizability of a Square Matrix or a Linear Operator
...... 793
B.12 Canonical Forms for Matrices: Jordan Form and Rational Form
. . . 799
B.12.1 Jordan canonical form
...................... 799
B.12.2 Rational canonical form
..................... 809
References
..................................... 819
Index of Notations
................................ 823
Index
....................................... 839
CONTENTS
Preface to Volmne One.
.........................
vii
Preface to Volume Two
......................... xxi
Volume- Two
Part II: The Euclidean Structures of
R1. Ä2,
and K3
1
Chapter
4
The Euclidean Plane R 2
................... 27
Introduction
............................... 27
Sketch of the Content
.......................... 35
4.1
Straight Lines
........................... 36
4.2
Circles
............................... 45
4.3
Geometric Definition of the Real Determinant of Order
2 . . 53
4.4
Noimatural Inner Products: Positive-Definite and Orthogonal
Matrices
.............................. 67
1.5
Tlu1
Singular Value Decomposition: The Polar Decomposition
and the Generalized Inverse of a Matrix
............ 87
4.
G
Linear Functional and
(Selí-)
Adjoint Linear Operator
.... 120
4.7
Diagonalizability of a Symmetric Matrix of Order
2...... 146
4.8
The Euclidean Transformation (or Rigid Motion)
....... 161
4.0
Euclidean Invariants and Euclidean Geometry
......... 194
4.10
Quadratic Curves
......................... 210
Chapter
5
The Euclidean Space R3
.................. 239
Introduction
............................... 239
Sketch of the Content
.......................... 252
5.1
The Exterior (or Vector) Product
................ 255
5.2
Lines. Planes, and Spheres
.................... 272
5.3
Geometric Definition of the Real Determinant of Order
3 . . 295
xxvi Contents
5.4 Noniiatural Inner Products:
Posi
t
і
ve-
Deri
ni t
e
and Orthogonal
Matrices
.............................. 331
5.5
The Singular Value Decomposition: The Polar Decomposition
and the Generalized Inverse of a Matrix
............ 380
5.6
Linear Functional and (Self-) Adjoint Linear Operator
.... 410
5.7
Diagonalizability of a Symmetric Matrix of Order
3 ..... 426
5.8
The Euclidean Transformation (or Rigid Motion)
....... 519
5.9
Euclidean Invariants and Euclidean Geometry
......... 547
5.9.1
Distances from a point to a plane and between planes
553
*5 .9.2 Angles between planes
.................. 572
*5.9.3 A -parallelogram:
Aľ-vector
................. 591
*5.9.4 The geometry and trigonometry of fc-simplex
(tetrahedron)
....................... 611
*5.9.5
В
ary
cent
rie
coordinates
................. 628
5.10
Quadrics
.............................. 646
*5.11 Elliptic (or Spherical) Geometry
................ 693
*5.12 Hyperbolic Geometry
....................... 722
Appendix
Contents of Volume One
......................... 767
Errata to Volume One
.......................... 771
References
................................. 773
Index of Notations
............................ 777
Index
................................... 791
|
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| spelling | Lin, I-Hsiung Verfasser (DE-588)1015369472 aut Geometric linear algebra I-Hsiung Lin New Jersey World Scientific txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and indexes Algebras, Linear Textbooks Geometry, Algebraic Textbooks Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Lineare Algebra (DE-588)4035811-2 s Algebraische Geometrie (DE-588)4001161-6 s DE-604 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013101051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lin, I-Hsiung Geometric linear algebra Algebras, Linear Textbooks Geometry, Algebraic Textbooks Algebraische Geometrie (DE-588)4001161-6 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4035811-2 (DE-588)4123623-3 |
| title | Geometric linear algebra |
| title_auth | Geometric linear algebra |
| title_exact_search | Geometric linear algebra |
| title_full | Geometric linear algebra I-Hsiung Lin |
| title_fullStr | Geometric linear algebra I-Hsiung Lin |
| title_full_unstemmed | Geometric linear algebra I-Hsiung Lin |
| title_short | Geometric linear algebra |
| title_sort | geometric linear algebra |
| topic | Algebras, Linear Textbooks Geometry, Algebraic Textbooks Algebraische Geometrie (DE-588)4001161-6 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Textbooks Geometry, Algebraic Textbooks Algebraische Geometrie Lineare Algebra Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013101051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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