2026-09-19T08:04:37Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1433452022-06-16T03:10:52Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Sra, Suvrit
Poorya Habibzadeh
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2022-06-15T13:14:07Z
2022-06-15T13:14:07Z
2022-02
2022-03-04T20:59:51.377Z
https://hdl.handle.net/1721.1/143345
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.
S.M.
Massachusetts Institute of Technology
In Copyright - Educational Use Permitted
Copyright MIT
http://rightsstatements.org/page/InC-EDU/1.0/
Discrepancy Values and their Applications
Thesis
application/pdf
Master
Master of Science in Electrical Engineering and Computer Science
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="c9ccbf95-c8a7-4a03-bb3d-530eb5ad149d">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Title>Discrepancy Values and their Applications</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2022-02</PublicationDate>
<Authors>
<Author>
<DisplayName>Poorya Habibzadeh</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://rightsstatements.org/page/InC-EDU/1.0/</License>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>