dc.contributor.advisor | Landsberg, Joseph | |
dc.creator | Qi, Yang | |
dc.date.accessioned | 2013-12-16T20:09:27Z | |
dc.date.available | 2013-12-16T20:09:27Z | |
dc.date.created | 2013-08 | |
dc.date.issued | 2013-07-17 | |
dc.date.submitted | August 2013 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/151240 | |
dc.description.abstract | Due to the exponential growth of the dimension of the space of tensors V_(1)⊗• • •⊗V_(n), any naive method of representing these tensors is intractable on a computer. In practice, we consider feasible subspaces (subvarieties) which are defined to reduce the storage cost and the computational complexity. In this thesis, we study two such types of subvarieties: the third secant variety of the product of n projective spaces, and tensor network states.
For the third secant variety of the product of n projective spaces, we determine set-theoretic defining equations, and give an upper bound of the degrees of these equations.
For tensor network states, we answer a question of L. Grasedyck that arose in quantum information theory, showing that the limit of tensors in a space of tensor network states need not be a tensor network state. We also give geometric descriptions of spaces of tensor networks states corresponding to trees and loops. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.subject | The third secant varieties of Segre varieties | en |
dc.subject | defining equations | en |
dc.subject | tensor network states | en |
dc.subject | geometric complexity theory | en |
dc.title | Geometry of Feasible Spaces of Tensors | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A & M University | en |
thesis.degree.name | Doctor of Philosophy | en |
thesis.degree.level | Doctoral | en |
dc.contributor.committeeMember | Sottile, Frank | |
dc.contributor.committeeMember | Lima-Filho, Paulo | |
dc.contributor.committeeMember | Robles, Colleen | |
dc.contributor.committeeMember | Becker, Katrin | |
dc.type.material | text | en |
dc.date.updated | 2013-12-16T20:09:27Z | |