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THE COMMUTING TRIPLES OF MATRICES
by
Yongho Han
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful¯llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2007
Copyright 2007 Yongho Han
Object Description
| Title | The commuting triples of matrices |
| Author | Han, Yongho |
| Author email | yhh@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2007-04-02 |
| Date submitted | 2007 |
| Restricted until | Unrestricted |
| Date published | 2007-06-05 |
| Advisor (committee chair) | Guralnick, Robert |
| Advisor (committee member) |
Montgomery, Susan Huang, Ming-Deh |
| Abstract | The irreducibility of the variety C(m,n) commuting m-tuples of n X n matrices has been studied by several authors. It is known that this variety is irreducible if m=2, n=1,2,3 and reducible if m,n>=4. The irreducibility of C(3,n) was asked by Gersteinhaber. Until now we know that C(3,n) is reducible for n>=32, but irreducible for n<=4. -- If the characteristic of an arbitrary algebraically closed field is zero, then we have more specific answer for this question. In this case C(3,n) is reducible for n>=30 and irreducible for n<=6. -- This dissertation is primarily concerned with the study of the variety C(3,7). We show that this variety is also irreducible. Guralnick and Omladi\v{c} have conjectured that it is reducible for n > 7 |
| Keyword | irreducible variety of commuting triples; approximation by generic matrices |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m510 |
| Rights | Han, Yongho |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Han-20070605 |
| Archival file | uscthesesreloadpub_Volume44/etd-Han-20070605.pdf |
Description
| Title | Page 1 |
| Full text | THE COMMUTING TRIPLES OF MATRICES by Yongho Han A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful¯llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATHEMATICS) August 2007 Copyright 2007 Yongho Han |
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