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

Transforming a binary vector

  1. Dec 19, 2011 #1
    Hi,

    This is my first post and I must worn you that I'm not a mathematician. Im just a regular blonk looking for help concerning the following problem.

    What i have is a set (T) of binary vectors:


    A: 100110
    B: 000110
    C: 010110


    now what i am trying to figure out is there a transformation, a function to transform given vectors in such a way that

    A>B>C

    where a relation > on T is given by the fact that to convert

    B->A takes 1 step
    C->A takes 2 steps
    C->B takes 1 step

    Can anyone suggest a book or a paper where such things are discussed , or give a few pointers?

    Thank you,

    baxy

    PS

    and the relation can ba symmetrical

    A<B<C

    as long as the order is preserved
     
    Last edited: Dec 19, 2011
  2. jcsd
  3. Dec 19, 2011 #2

    chiro

    User Avatar
    Science Advisor

    Hey baxy and welcome to the forums.

    I'm not exactly sure what you are trying to do, but it seems that you're given a set T = {T1,T2,T3} and you want to find a transformation that takes T1,T2,T3 in which f(T1) > f(T2) > f(T3) or f(T1) < f(T2) < f(T3).

    One easy transformation that comes to mind if we assume that all entries of the set are non-zero is to use a transformation that maps an input vector to an output vector. In other words, using your set with three elements define F to be:

    F(T1,T2,T3) = [T1+T2+T3,T2+T3,T3] where the output is a vector with three elements.

    Since this is a linear transformation, you can create an appropriate matrix that represents this transformation and define that as your operator.

    Is this what you had in mind?

    Also I didn't take into account the binary nature of your number, so you would have to compensate for this in your computation.
     
  4. Dec 19, 2011 #3
    ok, but i didn't quite understand how can i from this output vector figure out that T1>T2>T3 ? so what i need t do is transform my vectors into something and then just by sorting the transforms, figure out that T1_{A} needs 1 transformation step to be converted to T2_{B} and 2 transformation step to be converted to T3_{C}.

    This is my problem.
     
  5. Dec 19, 2011 #4

    chiro

    User Avatar
    Science Advisor

    Ohh I see what you mean.

    Well to sort two elements the first one is min(T1,T2) and the last is max(T1,T2). Can you adapt this for three elements?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Transforming a binary vector
  1. Vector Transformation (Replies: 1)

  2. Vector transformation (Replies: 3)

Loading...