Vectors and matrices:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Menasha, Wis.
Math. Assoc. of America
1966
|
| Ausgabe: | 6. impr. |
| Schriftenreihe: | The Carus mathematical monographs.
7. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 203 S. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804119206202966016 |
|---|---|
| adam_text | TABLE OF CONTENTS
CHAPTER PAGE
I. Systems of Linear Equations
1. Graphs 3
2. Equivalence of systems 6
3. Elementary operations 8
4. Systems of homogeneous equations 8
5. Systems of non homogeneous equations .... 11
II. Vector Spaces
6. Vectors in ordinary space 15
7. Vectors in general 17
8. Rank of a linear system 21
9. The concept of matrix 23
10. Rectangular arrays 29
11. Elementary matrices 31
12. A normal form 35
13. Non singular matrices 38
14. Column vectors 40
15. Systems of equations 43
16. On the rank of a product 44
III. Determinants
17. Complex numbers 47
18. Matrices as hypercomplex numbers 49
19. Determinants 54
20. The adjoint 56
21. Properties of determinants 61
22. Minors and cofactors 63
23. Rank 64
IV. Matric Polynomials
24. Ring with unit element 67
25. Polynomial domains 68
26. Degree of a polynomial 71
27. Matrices with polynomial elements 74
ix
x CONTENTS
CHAPTER PAGE
28. The characteristic function 75
29. The minimum function 77
30. The rank of a polynomial in a matrix .... 79
31. Matrix having a given minimum function ... 81
32. The norm 82
V. Union and Intersection
33. Complementary spaces 86
34. Linear homogeneous systems 88
35. Union and intersection 90
36. Divisors and multiples 95
37. Divisors and multiples of matric polynomials . . 99
38. Relation of the union to the greatest common right
divisor 100
39. The sum of vector spaces 102
40. Annihilators of vectors 106
VI. The Rational Canonical Form
41. Similar matrices 112
42. The direct sum 114
43. Invariant spaces 116
44. The non derogatory case 122
45. A canonical form 125
46. The derogatory case 128
47. Continuation of the derogatory case 131
48. The rational canonical form 133
VII. Elementary Divisors
49. Equivalence of matrices 137
50. Invariant factors 139
51. A canonical form 141
52. Elementary divisors 144
53. Elementary divisors of a direct sum 147
54. Similar matrices 148
55. The Weyr characteristic 150
56. Collineations 155
VIII. Orthogonal Transformations
57. Orthogonal matrices 160
58. Orthogonal bases 162
CONTENTS »
CHAPTER . PAGE
59. Symmetric matrices 166
60. The orthogonal canonical form 169
61. Principal axis transformation 171
IX. Endomorphisms
62. Groups with operators 175
63. Vector fields 179
64. Matrices 183
65. Change of basis 186
Bibliography 189
Index 191
Problems 193
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| author | MacDuffee, Cyrus C. |
| author_facet | MacDuffee, Cyrus C. |
| author_role | aut |
| author_sort | MacDuffee, Cyrus C. |
| author_variant | c c m cc ccm |
| building | Verbundindex |
| bvnumber | BV005089748 |
| classification_rvk | SK 220 |
| ctrlnum | (OCoLC)67597735 (DE-599)BVBBV005089748 |
| discipline | Mathematik |
| edition | 6. impr. |
| format | Book |
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| id | DE-604.BV005089748 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:22:30Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003120487 |
| oclc_num | 67597735 |
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| owner | DE-473 DE-BY-UBG DE-355 DE-BY-UBR |
| owner_facet | DE-473 DE-BY-UBG DE-355 DE-BY-UBR |
| physical | XI, 203 S. |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Math. Assoc. of America |
| record_format | marc |
| series | The Carus mathematical monographs. |
| series2 | The Carus mathematical monographs. |
| spelling | MacDuffee, Cyrus C. Verfasser aut Vectors and matrices Cyrus Colton MacDuffee* 6. impr. Menasha, Wis. Math. Assoc. of America 1966 XI, 203 S. txt rdacontent n rdamedia nc rdacarrier The Carus mathematical monographs. 7. Vektor (DE-588)4202708-1 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Vektorrechnung (DE-588)4062471-7 gnd rswk-swf Vektor (DE-588)4202708-1 s Matrix Mathematik (DE-588)4037968-1 s DE-604 Vektorrechnung (DE-588)4062471-7 s 1\p DE-604 The Carus mathematical monographs. 7. (DE-604)BV001887236 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003120487&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 | MacDuffee, Cyrus C. Vectors and matrices The Carus mathematical monographs. Vektor (DE-588)4202708-1 gnd Matrix Mathematik (DE-588)4037968-1 gnd Vektorrechnung (DE-588)4062471-7 gnd |
| subject_GND | (DE-588)4202708-1 (DE-588)4037968-1 (DE-588)4062471-7 |
| title | Vectors and matrices |
| title_auth | Vectors and matrices |
| title_exact_search | Vectors and matrices |
| title_full | Vectors and matrices Cyrus Colton MacDuffee* |
| title_fullStr | Vectors and matrices Cyrus Colton MacDuffee* |
| title_full_unstemmed | Vectors and matrices Cyrus Colton MacDuffee* |
| title_short | Vectors and matrices |
| title_sort | vectors and matrices |
| topic | Vektor (DE-588)4202708-1 gnd Matrix Mathematik (DE-588)4037968-1 gnd Vektorrechnung (DE-588)4062471-7 gnd |
| topic_facet | Vektor Matrix Mathematik Vektorrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003120487&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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