國立虎尾科技大學 |

Variants of Zero Forcing and Their Applications to the Minimum Rank Problem.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Variants of Zero Forcing and Their Applications to the Minimum Rank Problem./
Author:	Lin, Chin-Hung.
Description:	1 online resource (75 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
Contained By:	Dissertation Abstracts International78-11B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369878820

Variants of Zero Forcing and Their Applications to the Minimum Rank Problem.
Lin, Chin-Hung.

Variants of Zero Forcing and Their Applications to the Minimum Rank Problem. - 1 online resource (75 pages)

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

The minimum rank problem refers to finding the smallest possible rank, or equivalently the largest possible nullity, among matrices under certain restrictions. These restrictions can be the zero-nonzero pattern, conditions on the inertia, or other properties of a matrix. Zero forcing is a powerful technique for controlling the nullity and plays a significant role in the minimum rank problem. This thesis introduces several zero forcing parameters and their applications on the minimum rank problem.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369878820Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Variants of Zero Forcing and Their Applications to the Minimum Rank Problem.
LDR:03167ntm a2200361Ki 4500 001 909708
005 20180426091044.5
006 m o u
007 cr mn||||a|a||
008 190606s2017 xx obm 000 0 eng d
020 $a 9781369878820
035 $a (MiAaPQ)AAI10259647
035 $a (MiAaPQ)iastate:16290
035 $a AAI10259647
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Lin, Chin-Hung. $3 1180621
245 1 0 $a Variants of Zero Forcing and Their Applications to the Minimum Rank Problem.
264 0 $c 2017
300 $a 1 online resource (75 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
500 $a Advisers: Leslie Hogben; Steve Butler.
502 $a Thesis (Ph.D.) $c Iowa State University $d 2017.
504 $a Includes bibliographical references
520 $a The minimum rank problem refers to finding the smallest possible rank, or equivalently the largest possible nullity, among matrices under certain restrictions. These restrictions can be the zero-nonzero pattern, conditions on the inertia, or other properties of a matrix. Zero forcing is a powerful technique for controlling the nullity and plays a significant role in the minimum rank problem. This thesis introduces several zero forcing parameters and their applications on the minimum rank problem.
520 $a Zero-nonzero patterns can be described by graphs: The edges (including the loops) represent the nonzero entries, while the non-edges correspond to the zero entries. For simple graphs, where no loops are allowed, the diagonal entries can be any real numbers. The maximum nullity of a graph is the maximum nullity among symmetric matrices with the pattern described by the graph. In Chapter 2, the odd cycle zero forcing number Z oc(G) and the enhanced odd cycle zero forcing number Zˆoc(G) are introduced as bounds for the maximum nullities of loop graphs G and simple graphs G, respectively. Also, a relation between loop graphs and simple graphs through graph blowups is developed.
520 $a The Colin de Verdiere type parameter zeta(G) is defined as the maximum nullity of real symmetric matrices A with the pattern described by G and with the Strong Arnold Property (SAP), which means X = O is the only symmetric matrix that satisfies A · X = I · X = AX = O (here · is the entrywise product). Chapter 3 introduces zero forcing parameters ZSAP(G) and Zvc(G); we show that Z SAP(G) = 0 implies every symmetric matrix with the pattern described by Gf has the SAP and that the inequality M(G) -- Zvc(G) ≤ zeta(G) holds for every graph G. Also, the values of zeta( G) are computed for all graphs up to 7 vertices, establishing zeta( G) = [Z](G) for these graphs.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Iowa State University. $b Mathematics. $3 1179234
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10259647 $z click for full text (PQDT)