URN |
etd-0709107-162359 |
Author |
Chih-jen Wang |
Author's Email Address |
No Public. |
Statistics |
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Department |
Applied Mathematics |
Year |
2006 |
Semester |
2 |
Degree |
Master |
Type of Document |
|
Language |
English |
Title |
On the invertibility of linear sums of two idempotents and of two square zero operators |
Date of Defense |
2007-06-15 |
Page Count |
35 |
Keyword |
partial isometry
idempotent
n-potent
invertibility
nilpotent
square-zero operator
|
Abstract |
Let P and Q be two idempotents, we review the results about the equivalence between the invertibility of a linear combination aP +bQ and that of P +Q, where a and b are any nonzero complex numbers with a + b eq 0. It is possible to extend the results to the case P and Q are square-zero elements. However, we will show that these extensions are impossible in general for P and Q being partial isometries or n-potents with n geq 3. We will show in case P and Q are square-zero elements, the invertibility of P +Q is equivalent to that of aP +bQ for nonzero a, b. |
Advisory Committee |
Mark C. Ho - chair
Mu-Ming Wong - co-chair
Jyh-Shyang Jeang - co-chair
Hwa-Long Gau - co-chair
Ngai-Ching Wong - advisor
|
Files |
indicate accessible in a year |
Date of Submission |
2007-07-09 |