Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inverse transformation matrix entry bounds

  1. Jun 14, 2013 #1
    I have sets of 2d vectors to be transformed by an augmented matrix A that performs an affine transform.
    Matrix A can have values that differ at most |d| from the identity matrix, to limit the transformation, meaning that the min/max bounds for A are [itex] I_3 \pm dI_3[/itex]

    The problem is that i'd lke to have bounds for the inverse as well, expressed as a function of d, so that if i know that the transformation matrix is bound by d, that the matrix of the inverse transformation is bound by f(d).
    I thought the same bounds would apply, but they don't.
    Is there a way to find them?
  2. jcsd
  3. Jun 15, 2013 #2
    Nobody replies :(
    Well i had the following idea:
    make a matrix [ A , eye(3) , MinBound , MaxBound] , and reduce it to row echelon form.
    That way the first 3x3 chunk will be eye(3) , the second the inverse of A , the third and fourth the respective min and max bounds for the inverse, hopefully.
  4. Jun 15, 2013 #3

    Stephen Tashi

    User Avatar
    Science Advisor

    Is d a scalar? Are you saying that A must be a diagonal matrix?
  5. Jun 15, 2013 #4


    User Avatar
    Science Advisor

    Hey atrus_ovis.

    Try setting up the augmented system and find the inverse through row-reduction or by using co-factors (Cramers Rule) and you'll get an answer in terms of d.
  6. Jun 16, 2013 #5
    It is a scalar.A is not a diagonal,it's an identity matrix, where each value is shifted by at least/most +/- d.

    Yup,that's what i did.
  7. Jun 16, 2013 #6

    Stephen Tashi

    User Avatar
    Science Advisor

    The expression [itex] I_3 \pm d I_3 [/itex] only adds or subtracts d to the diagonal elements of the identity matrix [itex] I_3 [/itex].
  8. Jun 18, 2013 #7
    You're right, i meant [itex] I_3 \pm \text{repmat(d,3,3)} [/itex] in matlabese.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Inverse transformation matrix entry bounds
  1. Matrix entries (Replies: 5)

  2. Inverse Matrix (Replies: 2)

  3. Inverse of a matrix (Replies: 4)

  4. Inverse of a matrix (Replies: 3)