Discrepancy Values and their Applications
Name
Habibzadeh-Pourya-SM-EECS-2022-thesis.pdf
Description
Thesis PDF
Size
602.9 KB
Format
Adobe PDF
Checksum (MD5)
05ab6ba22286767f5c2bd01bd9249e87
Author(s)
Poorya Habibzadeh
Advisor(s)
Sra, Suvrit
Date Issued
February 2022
Publisher
Massachusetts Institute of Technology
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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