1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrix logarithm

  1. Nov 25, 2013 #1
    1. The problem statement, all variables and given/known data

    Hi,
    how can i show that the matrix logarithm log(I+A) is continuously differentiable on the set of matrices having operator norm less than 1.



    2. Relevant equations

    http://planetmath.org/matrixlogarithm

    3. The attempt at a solution
    i tried to compute the derivative but it is awkward
     
  2. jcsd
  3. Nov 25, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Computing the derivative may be hard, but all you are being asked to do is to show that the derivative exists and is continuous.
     
  4. Nov 25, 2013 #3
    And how do i do that?
     
  5. Nov 25, 2013 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I'm afraid I cannot help you there; I know how to do it, but it is not my homework. I would, however, suggest that you write out a few terms of the log and see if the resulting polynomial is continuously differentiable---again, without necessarily being able to compute it convenienetly.
     
  6. Nov 25, 2013 #5
    I mean,continuously differentiable as an operator,that is, the derivative is continuous as a function of the matrix A.I will be glad if you send me a more specific hint.
     
  7. Nov 25, 2013 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Define what is meant by the derivative in this case.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Matrix logarithm
  1. Logarithm =/ (Replies: 10)

  2. Logarithmic Spirals (Replies: 3)

  3. Logarithm Derivatives (Replies: 3)

Loading...