Discrepancy Values and their Applications

In this thesis, we introduce the concept of discrepancy values for the square matrices. We prove several properties of such objects, together with their relationship with other operators of matrices, such as singular values. After creating a toolbox of results about the discrepancy values, we proceed by introducing some ways to compute the discrepancy values efficiently. We then employ these objects to achieve tight bounds on the norms of the commutator of two matrices and several other quantities. We finish the thesis by putting forward some conjectures regarding discrepancy values and discussing their implications.

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2022

Author dc:creator

• Poorya Habibzadeh

Advisor dc:contributor.advisor

• Sra, Suvrit

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright MIT

Licence dc:rights.uri

• http://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/143345

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/143345