What are tensors exactly?:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2021]
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| Schlagworte: | |
| Online-Zugang: | TUM01 |
| Beschreibung: | 1 Online-Ressource (xviii, 227 Seiten) Illustrationen, Diagramme |
| ISBN: | 9789811241024 9789811241031 9811241023 |
Internformat
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| 100 | 1 | |a Guo, Hongyu |e Verfasser |0 (DE-588)1258416220 |4 aut | |
| 245 | 1 | 0 | |a What are tensors exactly? |c Hongyu Guo |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2021] | |
| 300 | |a 1 Online-Ressource (xviii, 227 Seiten) |b Illustrationen, Diagramme | ||
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| 505 | 8 | |a Intro -- Contents -- Preface -- List of Boxes -- List of Figures -- Chapter Dependency Chart -- Notation -- Chapter 1. Confusions: What Are Tensors Exactly? -- 1. Questions and Confusions -- 2. Who Invented the Tensor? -- 3. Different Definitions of the Tensor -- 4. Plain Things by Fancy Tensor Names -- 5. Tensors without a Tensor Name-Linear Transformations -- 6. Comparison: Different Definitions of the Vector-Concrete Systems vs. Abstract Systems -- 7. Tensor Product and Tensor Spaces -- 8. Degree, Rank, Order or Dimension-Which Is the Best Name? | |
| 505 | 8 | |a *9. What Are Pseudo-Scalars, Pseudo-Vectors and Pseudo-Tensors Exactly? -- 10. What Is Tensor Analysis Exactly? Relation to Riemannian Geometry -- 10.1 Vector Analysis -- 10.2 Tensor Analysis and Riemannian Geometry -- Chapter 2. Why and How Are Tensors Used in Machine Learning? -- 1. How AlphaGo Beat the Best Human Go Player via Deep Learning -- 2. The Tensor Data Structure -- 2.1 AlphaGo -- 2.2 Images and Videos -- 2.3 Speech and Audio Applications -- 3. TensorFlow and the Tensor Processing Unit (TPU) -- 4. Is Tensor in Machine Learning a Hype? -- Chapter 3. Direct Sum Space U ⊕ V | |
| 505 | 8 | |a 1. The Elements -- 2. The Operations -- 3. The Dimension of U ⊕ V -- Chapter 4. Gibbs Dyadics -- 1. What Is a Dyad? -- 2. When Are Two Dyads Equal? -- 3. What Are the Operations on Dyads? -- 4. What Is a Dyadic? -- 5. What Are the Operations on Dyadics? -- 6. When Are Two Dyadics Equal? -- 7. Matrix Representation -- 8. Change of Coordinates -- 9. What Are the Meanings of Dyadics? Linear Transformations and Bilinear Forms -- 10. What Is the Nature of Dyadic Juxtaposition? -- Chapter 5. Tensor Spaces (Tensor Product U ⊕ V) -- 1. Bilinear Mappings | |
| 505 | 8 | |a 2. Differences: Bilinear Mapping vs. Linear Mapping -- 3. Multilinear Mappings -- 4. Tensor Product Space of Two Vector Spaces -- 5. Decomposable Tensors -- 6. Tensor Product of Linear Mappings -- 7. Tensor Product Space of Multiple Vector Spaces -- 8. Vector-valued Tensors-The Most General Model -- Chapter 6. Tensor Spaces (Tensor Power V⊕(p -- q)) -- 1. Tensor Spaces (Tensor Power Spaces) -- 2. Change of Basis -- 3. Induced Inner Product -- 4. Lowering and Raising Indices-Isomorphisms -- Chapter 7. Tensor Algebra -- 1. Tensor Product of Tensors -- 2. Tensor Algebra | |
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| 776 | 0 | 8 | |i Erscheint auch als |a Guo, Hongyu |t What Are Tensors Exactly? |d Singapore : World Scientific Publishing Company,c2021 |n Druck-Ausgabe, Hardcover |z 978-981-124-101-7 |
| 912 | |a ZDB-124-WOP | ||
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Datensatz im Suchindex
| _version_ | 1804184264718155776 |
|---|---|
| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Guo, Hongyu |
| author_GND | (DE-588)1258416220 |
| author_facet | Guo, Hongyu |
| author_role | aut |
| author_sort | Guo, Hongyu |
| author_variant | h g hg |
| building | Verbundindex |
| bvnumber | BV048382741 |
| classification_rvk | SK 370 |
| classification_tum | MAT 150 |
| collection | ZDB-124-WOP |
| contents | Intro -- Contents -- Preface -- List of Boxes -- List of Figures -- Chapter Dependency Chart -- Notation -- Chapter 1. Confusions: What Are Tensors Exactly? -- 1. Questions and Confusions -- 2. Who Invented the Tensor? -- 3. Different Definitions of the Tensor -- 4. Plain Things by Fancy Tensor Names -- 5. Tensors without a Tensor Name-Linear Transformations -- 6. Comparison: Different Definitions of the Vector-Concrete Systems vs. Abstract Systems -- 7. Tensor Product and Tensor Spaces -- 8. Degree, Rank, Order or Dimension-Which Is the Best Name? *9. What Are Pseudo-Scalars, Pseudo-Vectors and Pseudo-Tensors Exactly? -- 10. What Is Tensor Analysis Exactly? Relation to Riemannian Geometry -- 10.1 Vector Analysis -- 10.2 Tensor Analysis and Riemannian Geometry -- Chapter 2. Why and How Are Tensors Used in Machine Learning? -- 1. How AlphaGo Beat the Best Human Go Player via Deep Learning -- 2. The Tensor Data Structure -- 2.1 AlphaGo -- 2.2 Images and Videos -- 2.3 Speech and Audio Applications -- 3. TensorFlow and the Tensor Processing Unit (TPU) -- 4. Is Tensor in Machine Learning a Hype? -- Chapter 3. Direct Sum Space U ⊕ V 1. The Elements -- 2. The Operations -- 3. The Dimension of U ⊕ V -- Chapter 4. Gibbs Dyadics -- 1. What Is a Dyad? -- 2. When Are Two Dyads Equal? -- 3. What Are the Operations on Dyads? -- 4. What Is a Dyadic? -- 5. What Are the Operations on Dyadics? -- 6. When Are Two Dyadics Equal? -- 7. Matrix Representation -- 8. Change of Coordinates -- 9. What Are the Meanings of Dyadics? Linear Transformations and Bilinear Forms -- 10. What Is the Nature of Dyadic Juxtaposition? -- Chapter 5. Tensor Spaces (Tensor Product U ⊕ V) -- 1. Bilinear Mappings 2. Differences: Bilinear Mapping vs. Linear Mapping -- 3. Multilinear Mappings -- 4. Tensor Product Space of Two Vector Spaces -- 5. Decomposable Tensors -- 6. Tensor Product of Linear Mappings -- 7. Tensor Product Space of Multiple Vector Spaces -- 8. Vector-valued Tensors-The Most General Model -- Chapter 6. Tensor Spaces (Tensor Power V⊕(p -- q)) -- 1. Tensor Spaces (Tensor Power Spaces) -- 2. Change of Basis -- 3. Induced Inner Product -- 4. Lowering and Raising Indices-Isomorphisms -- Chapter 7. Tensor Algebra -- 1. Tensor Product of Tensors -- 2. Tensor Algebra |
| ctrlnum | (OCoLC)1344252573 (DE-599)BVBBV048382741 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV048382741 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:19:24Z |
| indexdate | 2024-07-10T09:36:35Z |
| institution | BVB |
| isbn | 9789811241024 9789811241031 9811241023 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033761558 |
| oclc_num | 1344252573 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 1 Online-Ressource (xviii, 227 Seiten) Illustrationen, Diagramme |
| psigel | ZDB-124-WOP ZDB-124-WOP TUM_Einzelkauf_2022 |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Guo, Hongyu Verfasser (DE-588)1258416220 aut What are tensors exactly? Hongyu Guo New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2021] 1 Online-Ressource (xviii, 227 Seiten) Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Intro -- Contents -- Preface -- List of Boxes -- List of Figures -- Chapter Dependency Chart -- Notation -- Chapter 1. Confusions: What Are Tensors Exactly? -- 1. Questions and Confusions -- 2. Who Invented the Tensor? -- 3. Different Definitions of the Tensor -- 4. Plain Things by Fancy Tensor Names -- 5. Tensors without a Tensor Name-Linear Transformations -- 6. Comparison: Different Definitions of the Vector-Concrete Systems vs. Abstract Systems -- 7. Tensor Product and Tensor Spaces -- 8. Degree, Rank, Order or Dimension-Which Is the Best Name? *9. What Are Pseudo-Scalars, Pseudo-Vectors and Pseudo-Tensors Exactly? -- 10. What Is Tensor Analysis Exactly? Relation to Riemannian Geometry -- 10.1 Vector Analysis -- 10.2 Tensor Analysis and Riemannian Geometry -- Chapter 2. Why and How Are Tensors Used in Machine Learning? -- 1. How AlphaGo Beat the Best Human Go Player via Deep Learning -- 2. The Tensor Data Structure -- 2.1 AlphaGo -- 2.2 Images and Videos -- 2.3 Speech and Audio Applications -- 3. TensorFlow and the Tensor Processing Unit (TPU) -- 4. Is Tensor in Machine Learning a Hype? -- Chapter 3. Direct Sum Space U ⊕ V 1. The Elements -- 2. The Operations -- 3. The Dimension of U ⊕ V -- Chapter 4. Gibbs Dyadics -- 1. What Is a Dyad? -- 2. When Are Two Dyads Equal? -- 3. What Are the Operations on Dyads? -- 4. What Is a Dyadic? -- 5. What Are the Operations on Dyadics? -- 6. When Are Two Dyadics Equal? -- 7. Matrix Representation -- 8. Change of Coordinates -- 9. What Are the Meanings of Dyadics? Linear Transformations and Bilinear Forms -- 10. What Is the Nature of Dyadic Juxtaposition? -- Chapter 5. Tensor Spaces (Tensor Product U ⊕ V) -- 1. Bilinear Mappings 2. Differences: Bilinear Mapping vs. Linear Mapping -- 3. Multilinear Mappings -- 4. Tensor Product Space of Two Vector Spaces -- 5. Decomposable Tensors -- 6. Tensor Product of Linear Mappings -- 7. Tensor Product Space of Multiple Vector Spaces -- 8. Vector-valued Tensors-The Most General Model -- Chapter 6. Tensor Spaces (Tensor Power V⊕(p -- q)) -- 1. Tensor Spaces (Tensor Power Spaces) -- 2. Change of Basis -- 3. Induced Inner Product -- 4. Lowering and Raising Indices-Isomorphisms -- Chapter 7. Tensor Algebra -- 1. Tensor Product of Tensors -- 2. Tensor Algebra Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Electronic books Tensorrechnung (DE-588)4192487-3 s DE-604 Erscheint auch als Guo, Hongyu What Are Tensors Exactly? Singapore : World Scientific Publishing Company,c2021 Druck-Ausgabe, Hardcover 978-981-124-101-7 |
| spellingShingle | Guo, Hongyu What are tensors exactly? Intro -- Contents -- Preface -- List of Boxes -- List of Figures -- Chapter Dependency Chart -- Notation -- Chapter 1. Confusions: What Are Tensors Exactly? -- 1. Questions and Confusions -- 2. Who Invented the Tensor? -- 3. Different Definitions of the Tensor -- 4. Plain Things by Fancy Tensor Names -- 5. Tensors without a Tensor Name-Linear Transformations -- 6. Comparison: Different Definitions of the Vector-Concrete Systems vs. Abstract Systems -- 7. Tensor Product and Tensor Spaces -- 8. Degree, Rank, Order or Dimension-Which Is the Best Name? *9. What Are Pseudo-Scalars, Pseudo-Vectors and Pseudo-Tensors Exactly? -- 10. What Is Tensor Analysis Exactly? Relation to Riemannian Geometry -- 10.1 Vector Analysis -- 10.2 Tensor Analysis and Riemannian Geometry -- Chapter 2. Why and How Are Tensors Used in Machine Learning? -- 1. How AlphaGo Beat the Best Human Go Player via Deep Learning -- 2. The Tensor Data Structure -- 2.1 AlphaGo -- 2.2 Images and Videos -- 2.3 Speech and Audio Applications -- 3. TensorFlow and the Tensor Processing Unit (TPU) -- 4. Is Tensor in Machine Learning a Hype? -- Chapter 3. Direct Sum Space U ⊕ V 1. The Elements -- 2. The Operations -- 3. The Dimension of U ⊕ V -- Chapter 4. Gibbs Dyadics -- 1. What Is a Dyad? -- 2. When Are Two Dyads Equal? -- 3. What Are the Operations on Dyads? -- 4. What Is a Dyadic? -- 5. What Are the Operations on Dyadics? -- 6. When Are Two Dyadics Equal? -- 7. Matrix Representation -- 8. Change of Coordinates -- 9. What Are the Meanings of Dyadics? Linear Transformations and Bilinear Forms -- 10. What Is the Nature of Dyadic Juxtaposition? -- Chapter 5. Tensor Spaces (Tensor Product U ⊕ V) -- 1. Bilinear Mappings 2. Differences: Bilinear Mapping vs. Linear Mapping -- 3. Multilinear Mappings -- 4. Tensor Product Space of Two Vector Spaces -- 5. Decomposable Tensors -- 6. Tensor Product of Linear Mappings -- 7. Tensor Product Space of Multiple Vector Spaces -- 8. Vector-valued Tensors-The Most General Model -- Chapter 6. Tensor Spaces (Tensor Power V⊕(p -- q)) -- 1. Tensor Spaces (Tensor Power Spaces) -- 2. Change of Basis -- 3. Induced Inner Product -- 4. Lowering and Raising Indices-Isomorphisms -- Chapter 7. Tensor Algebra -- 1. Tensor Product of Tensors -- 2. Tensor Algebra Tensorrechnung (DE-588)4192487-3 gnd |
| subject_GND | (DE-588)4192487-3 |
| title | What are tensors exactly? |
| title_auth | What are tensors exactly? |
| title_exact_search | What are tensors exactly? |
| title_exact_search_txtP | What are tensors exactly? |
| title_full | What are tensors exactly? Hongyu Guo |
| title_fullStr | What are tensors exactly? Hongyu Guo |
| title_full_unstemmed | What are tensors exactly? Hongyu Guo |
| title_short | What are tensors exactly? |
| title_sort | what are tensors exactly |
| topic | Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Tensorrechnung |
| work_keys_str_mv | AT guohongyu whataretensorsexactly |