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Linear transformation / analysis help

  1. Jun 6, 2005 #1
    Hi,

    I have that

    |T(p)| <= sqrt(10)*|p|

    where T is a linear mapping. The question is: How small must |p' - p''| be in order that |T(p') - T(p'')| <= 1/10.

    This is what I did:

    T linear, so

    |T(p') - T(p'')| = |T(p' - p'')|.

    Applying the bound:

    |T(p' - p'')| <= sqrt(10)*|p' - p''|

    So pick |p' - p''| = 1 / (sqrt(10)*10).

    Then

    |T(p' - p'')| = |T(p') - T(p'')| <= 1/10.

    Is that right?
     
  2. jcsd
  3. Jun 6, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    It looks okay to me.

    Daniel.
     
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