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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

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

    chiro

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    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

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    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.
     
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