|Mar31-07, 01:27 AM||#1|
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.
|Mar31-07, 04:35 AM||#2|
|Mar31-07, 05:44 AM||#3|
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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