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Homework Help: Transformation Matrix

  1. Mar 31, 2007 #1

    danago

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    Gold Member

    Given a transformation matrix T, which maps objects (x,y) to the image (x',y'). The inverse of T will map the image back to the object.

    Just wondering, what happens if matrix T is singular i.e. det(T)=0? Then there is no matrix to map the images back to the object.

    My teacher said that he thinks a transformation matrix will never be singular, but he wasnt 100% sure, so im just wanting to confirm.

    Thanks,
    Dan.
     
  2. jcsd
  3. Mar 31, 2007 #2

    radou

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    Homework Helper

    If, by "transformation matrix", you mean the matrix representation of a linear operator, then of course it can be singular. Think of the mapping A : x --> 0, for every x from the domain.
     
  4. Mar 31, 2007 #3

    HallsofIvy

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    Science Advisor

    That depends on what you mean by "transformation". The usual definition in Linear Algebra is simply that L(au+ bv)= aL(u)+ bL(v), which includes transformations that do not have inverses.

    On the other hand, if you require that the "transformation" change any n-dimensional object to another n-dimensional object, then it is non-singular.
    A singular transformation, such as a projection onto a plane or line, will map n-dimensional objects in to lower dimensionals objects and has no inverse.
     
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