Title page for etd-0709107-162359


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URN etd-0709107-162359
Author Chih-jen Wang
Author's Email Address No Public.
Statistics This thesis had been viewed 5060 times. Download 1093 times.
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
  • etd-0709107-162359.pdf
  • indicate accessible in a year
    Date of Submission 2007-07-09

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