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Tensors: Geometry and Applications
About this Title
J. M. Landsberg, Texas A&M University, College Station, TX
Publication: Graduate Studies in Mathematics
Publication Year:
2012; Volume 128
ISBNs: 978-0-8218-6907-9 (print); 978-0-8218-8483-6 (online)
DOI: https://doi.org/10.1090/gsm/128
MathSciNet review: MR2865915
MSC: Primary 15-01; Secondary 14N05, 15A69, 20G05
Table of Contents
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Front/Back Matter
Part 1. Motivation from applications, multilinear algebra and elementary results
- Chapter 1. Introduction
- Chapter 2. Multilinear algebra
- Chapter 3. Elementary results on rank and border rank
Part 2. Geometry and representation theory
- Chapter 4. Algebraic geometry for spaces of tensors
- Chapter 5. Secant varieties
- Chapter 6. Exploiting symmetry: Representation theory for spaces of tensors
- Chapter 7. Tests for border rank: Equations for secant varieties
- Chapter 8. Additional varieties useful for spaces of tensors
- Chapter 9. Rank
- Chapter 10. Normal forms for small tensors
Part 3. Applications
- Chapter 11. The complexity of matrix multiplication
- Chapter 12. Tensor decomposition
- Chapter 13. $\mathbf {P}$ v. $\mathbf {NP}$
- Chapter 14. Varieties of tensors in phylogenetics and quantum mechanics
Part 4. Advanced topics
- Chapter 15. Overview of the proof of the Alexander-Hirschowitz theorem
- Chapter 16. Representation theory
- Chapter 17. Weyman’s method
- Hints and answers to selected exercises