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Invariant lines?

  1. Jun 15, 2009 #1
    1. The problem statement, all variables and given/known data

    find in the form y= mx+c, the invariant lines of the tranformation with matrix

    [itex]
    \left(
    \begin{array}{cc}
    0 & 1 \\
    1 & 0
    \end{array}
    \right)[/itex]

    [itex]

    \left(
    \begin{array}{cc}
    0 & 1 \\
    1 & 0
    \end{array}
    \right)\left(
    \begin{array}{c}
    x \\
    \text{mx}+c
    \end{array}
    \right)=\left(
    \begin{array}{c}
    \text{mx}+c \\
    x
    \end{array}
    \right)

    [/itex]

    [itex] \Rightarrow x = m(mx+c)+c [/itex] Why???

    I just don't understand how that is implied in the first place and I don't have a method of working out invariant lines in the form mx or mx+c!
     
  2. jcsd
  3. Jun 15, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    Because you want a line whose x value will remain the same after undergoing the transformation.


    So when you multiply the matrix by (x,y) you get (y,x). You then want your line to have the the x value of the 'old y value'

    and if Y=MX+C

    X= mx+c

    so Y=M(mx+c) + C

    (I used capital letters to explain it better even though, the capitals are the same as the common ones)
     
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