Linear algebra and analytic geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. u.a.
Addison-Wesley
1971
|
| Series: | Addison-Wesley series in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 535 S. |
Staff View
MARC
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| 100 | 1 | |a Brinkmann, Heinrich W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear algebra and analytic geometry |c Heinrich W. Brinkmann ; Eugene A. Klotz |
| 264 | 1 | |a Reading, Mass. u.a. |b Addison-Wesley |c 1971 | |
| 300 | |a XVI, 535 S. | ||
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| 490 | 0 | |a Addison-Wesley series in mathematics | |
| 650 | 4 | |a Algèbre linéaire | |
| 650 | 4 | |a Géométrie analytique | |
| 650 | 4 | |a Algebras, Linear | |
| 650 | 4 | |a Geometry, Analytic | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
To the Reader .......... xv
Introduction
1 What is linear algebra? ......... 2
2 Why linear algebra? 3
3 The axiomatic method ......... 4
4 Mathematical models ......... 9
5 The relationship between mathematics and science . . . .12
Chapter 0 Preliminaries
1 Geometrical vectors . . . . . . . . .16
Supplement 1. Equivalence relations 18
Supplement 2. Groups 20
2 Vectors and A^ tuples ......... 22
3 Real functions .......... 24
4 Functions in general ......... 27
5 Composition of functions. Inverse functions 31
6 Fields 33
Chapter 1 Vector Spaces
1 In which the central characters are introduced 38
Supplement. Vector spaces over other fields 44
xi
2 Elementary properties of vector spaces 45
3 Subspaces 48
Supplement. The arithmetic of subspaces. ..... 53
4 Bases 56
Supplement. The deletion lemma, proof of 4.6 ..... 65
5 Isomorphic vector spaces ........ 66
Chapter 2 Matrices
1 Bases for subspaces ......... 73
2 The basis algorithm ......... 82
Supplement. Flow diagrams; a computer improvement ... 87
3* Matrix arithmetic 90
Supplement. Partitioned matrices ....... 96
4 Square matrices; transposition ....... 104
5* Some applications of matrix arithmetic ...... 121
Chapter 3 Linear Transformations
1 What they are 145
2 Arithmetic properties . . . . . . . . .153
3 Representing linear transformations. . . . . . .160
4 The dimension theorem; invertibility . . . . . .170
Supplement 1. Some consequences of the dimension theorem . .177
Supplement 2. Almost diagonal matrices . . . . .181
5* Dual spaces 182
Chapter 4 Systems of Linear Equations
1 An elementary approach . . . . . . . .187
2 Linear equations, matrices, and linear transformations . . . 201
3* Matrix equivalence; another solution procedure. .... 213
4* Change of basis 219
Chapter 5 Determinants
1 Definitions and the like 232
2 Calculations 241
3 Products and transpose ........ 248
4 Cofactors 254
5* Proof of existence and uniqueness 262
Chapter 6 The Eigenvalue Problem; Similar Matrices
1 Eigenvalues 267
Supplement 1. Gershgorin s theorem ...... 275
2 Distinct eigenvalues ......... 279
Supplement. The power method ....... 284
3 The characteristic polynomial ........ 289
4* Similarity ........... 293
5* An introduction to Jordan form ....... 299
6* Jordan form proofs; nilpotent matrices 307
Chapter 7 Linear Planes, and Other Flats
1 Points and Lines . . . . . . . . . .315
2 Parametric equations and affine equations ..... 329
3 Solutions to systems of linear equations ...... 336
Chapter 8 Euclidean Spaces
1 Distance, angles, and dot product ....... 345
2 Orthogonality 352
Supplement 1. Inner product spaces ...... 358
Supplement 2. Legendre polynomials ...... 360
Supplement 3. Complex inner product spaces..... 361
3* Orthogonal complements and flats again ..... 362
4* Distance from points to subspaces; least squares .... 370
5 Orthogonal linear transformations ...... 379
Supplement 1. Unitary mappings . ...... 386
Supplement 2. Orthogonal matrices expressed in terms of para¬
meters ........ 387
6* Rigid motions, especially in 2 and 3 space 388
Supplement. Rotation in R3; rotations and the cross product . . 402
7* Rigid motions in Un 406
Chapter 9 Symmetric Matrices and Quadratic Forms
1 Symmetric matrices and transformations 415
Supplement 1. Hermitian matrices ...... 421
Supplement 2. The Jacobi method 422
2 Quadratic forms ...••¦¦••• 425
3* The general 2nd degree equation 431
4 Positive definite matrices 443
5* Nonorthogonal diagonalization of quadratic forms .... 450
Chapter 10* Matrix Calculus
1 Vector norms 456
2 Matrix norms 466
Supplement 1. The spectral norm 471
Supplement 2. The row and column norms 476
3 Infinite series of matrices ........ 478
Supplement. eA+B 489
4 The complex numbers ......... 491
Supplement. Quaternions again ....... 496
5 Analogies between C and RnXn 499
Answers to Selected Exercises . . . . . . .511
Index 531
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:47:35Z |
| institution | BVB |
| language | English |
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| physical | XVI, 535 S. |
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| publishDate | 1971 |
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| publisher | Addison-Wesley |
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| series2 | Addison-Wesley series in mathematics |
| spelling | Brinkmann, Heinrich W. Verfasser aut Linear algebra and analytic geometry Heinrich W. Brinkmann ; Eugene A. Klotz Reading, Mass. u.a. Addison-Wesley 1971 XVI, 535 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Algèbre linéaire Géométrie analytique Algebras, Linear Geometry, Analytic Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Analytische Geometrie (DE-588)4001867-2 s DE-604 Klotz, Eugene A. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001686977&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brinkmann, Heinrich W. Klotz, Eugene A. Linear algebra and analytic geometry Algèbre linéaire Géométrie analytique Algebras, Linear Geometry, Analytic Lineare Algebra (DE-588)4035811-2 gnd Analytische Geometrie (DE-588)4001867-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4001867-2 |
| title | Linear algebra and analytic geometry |
| title_auth | Linear algebra and analytic geometry |
| title_exact_search | Linear algebra and analytic geometry |
| title_full | Linear algebra and analytic geometry Heinrich W. Brinkmann ; Eugene A. Klotz |
| title_fullStr | Linear algebra and analytic geometry Heinrich W. Brinkmann ; Eugene A. Klotz |
| title_full_unstemmed | Linear algebra and analytic geometry Heinrich W. Brinkmann ; Eugene A. Klotz |
| title_short | Linear algebra and analytic geometry |
| title_sort | linear algebra and analytic geometry |
| topic | Algèbre linéaire Géométrie analytique Algebras, Linear Geometry, Analytic Lineare Algebra (DE-588)4035811-2 gnd Analytische Geometrie (DE-588)4001867-2 gnd |
| topic_facet | Algèbre linéaire Géométrie analytique Algebras, Linear Geometry, Analytic Lineare Algebra Analytische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001686977&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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