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Numerical ranges and permanents.

Zhang, Fuzhen.

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Numerical ranges and permanents.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Numerical ranges and permanents./
Author:	Zhang, Fuzhen.
Description:	92 p.
Notes:	Chairperson: Robert C. Thompson.
Contained By:	Dissertation Abstracts International54-07B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9334897

Numerical ranges and permanents.
Zhang, Fuzhen.

Numerical ranges and permanents. - 92 p.

Chairperson: Robert C. Thompson.

Thesis (Ph.D.)--University of California, Santa Barbara, 1993.

In the first part of the dissertation we give a survey on matrices with quaternion entries, investigate the numerical ranges of quaternion matrices, and characterize the upper-bilds \sb+(A)$ of normal quaternion matrices. We show that Subjects--Topical Terms:

515831
Mathematics.

Numerical ranges and permanents.
LDR:01658nam 2200265 a 45 001 939870
005 20110517
008 110517s1993 ||||||||||||||||| ||eng d
035 $a (UMI)AAI9334897
035 $a AAI9334897
040 $a UMI $c UMI
100 1 $a Zhang, Fuzhen. $3 897328
245 1 0 $a Numerical ranges and permanents.
300 $a 92 p.
500 $a Chairperson: Robert C. Thompson.
500 $a Source: Dissertation Abstracts International, Volume: 54-07, Section: B, page: 3664.
502 $a Thesis (Ph.D.)--University of California, Santa Barbara, 1993.
520 $a In the first part of the dissertation we give a survey on matrices with quaternion entries, investigate the numerical ranges of quaternion matrices, and characterize the upper-bilds $b \sb+(A)$ of normal quaternion matrices. We show that $b \sb+(A)$ is the convex hull of the eigenvalues of A on the upper half plane, together with the interval $w (A) \ \cap R,$ where W(A) is the quaternionic numerical range of A.
520 $a In the second part of the dissertation we study the inequalities of permanents concerning the Hadamard product of positive semidefinite Hermitian matrices. Attempting to resolve a ten-year old open problem, we introduce an approach of maximizing matrices $m \sb{A}$ and prove that $m \sb{A}$ and $m \sb{A} \circ A$ are irreducible provided that A is irreducible, and we bring up more conjectures on permanents in the end.
590 $a School code: 0035.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a University of California, Santa Barbara. $3 1017586
773 0 $t Dissertation Abstracts International $g 54-07B.
790 $a 0035
790 1 0 $a Thompson, Robert C., $e advisor
791 $a Ph.D.
792 $a 1993
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9334897