Tensors: Geometry and Applications J.M. Landsberg - Texas A&M ...

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Contents Preface xi §0.1. Usage xi §0.2. Overview xii §0.3. Clash of cultures xvii §0.4. Further reading xviii §0.5. Conventions, acknowledgments xix Part 1. Motivation from applications, multilinear algebra and elementary results Chapter 1. Introduction 3 §1.1. The complexity of matrix multiplication 5 §1.2. Definitions from multilinear algebra 6 §1.3. Tensor decomposition 11 §1.4. P v. NP and algebraic variants 17 §1.5. Algebraic Statistics and tensor networks 21 §1.6. Geometry and representation theory 24 Chapter 2. Multilinear algebra 27 §2.1. Rust removal exercises 28 §2.2. Groups and representations 30 §2.3. Tensor products 32 §2.4. The rank and border rank of a tensor 35 §2.5. Examples of invariant tensors 39 v
Page 1: Tensors: Geometry and Applications
Page 5 and 6: Contents vii §5.4. The polynomial
Page 7 and 8: Contents ix Chapter 13. P v. NP 307
Page 9 and 10: Preface Tensors are ubiquitous in t
Page 11 and 12: 0.2. Overview xiii plays an especia
Page 13 and 14: 0.2. Overview xv tangential varieti
Page 15 and 16: 0.3. Clash of cultures xvii theorem
Page 17 and 18: 0.5. Conventions, acknowledgments x
Page 19: Part 1 Motivation from applications
Page 22 and 23: 4 1. Introduction data into a “mu
Page 24 and 25: 6 1. Introduction that by carefully
Page 26 and 27: 8 1. Introduction one can represent
Page 28 and 29: 10 1. Introduction to zero. Similar
Page 30 and 31: 12 1. Introduction Figure 1.3.1. te
Page 32 and 33: 14 1. Introduction the rank of this
Page 34 and 35: 16 1. Introduction observed there i
Page 36 and 37: 18 1. Introduction algebra class yo
Page 38 and 39: 20 1. Introduction Given a bipartit
Page 40 and 41: 22 1. Introduction throwing i for t
Page 42 and 43: 24 1. Introduction Just as phylogen
Page 45 and 46: Multilinear algebra Chapter 2 This
Page 47 and 48: 2.1. Rust removal exercises 29 This
Page 49 and 50: 2.2. Groups and representations 31
Page 51 and 52: 2.3. Tensor products 33 to V ⊗W
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2.4. The rank and border rank of a
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2.4. The rank and border rank of a
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2.5. Examples of invariant tensors
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2.6. Symmetric and skew-symmetric t
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2.7. Polynomials on the space of ma
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2.7. Polynomials on the space of ma
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2.8. Decomposition of V ⊗3 53 War
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2.9. Appendix: Basic definitions fr
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2.10. Appendix: Jordan and rational
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2.11. Appendix: Wiring diagrams 59
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