1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Represent a matrix on the (x,y)-plane

  1. Oct 2, 2005 #1

    hgj

    User Avatar

    I'm having trouble understanding how to represent a matrix on the (x,y)-plane. It seems like my classes expect me to know this, but I was never shown how. I've heard that there are a lot of connections between matrices and geometry, that matrices can be used to provide a geometric representation of something, but I don't understand how. For example, if I have a 2x2 matrix [tex]\left(\begin{array}{cc}x&y\\0&1\end{array}\right)[/tex], how does that look in the (x,y)-plane? I really want to understand this better.
     
  2. jcsd
  3. Oct 2, 2005 #2
    Well you could look at it as two vectors.
     
  4. Oct 2, 2005 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I have no idea what you mean by "represent a matrix on the xy-plane".

    Perhaps you mean "represent a matrix as a linear transformation on the xy-plane.

    If you are going to do that, it would be better not to have "x" and "y" in the matrix itself.
    If the matrix were [tex]\left(\begin{array}{cc}2&3\\0&1\end{array}\right)[/tex]
    for example then we could note that multiplying the "point" (x,y) by it gives
    [tex]\left(\begin{array}{cc}2&3\\0&1\end{array}\right)\left(\begin{array}{cc}x\\y\end{array}\right)= \left(\begin{array}{cc}2x+3y\\y\end{array}\right)[/tex]

    You could also, perhaps more simply, apply it to the "basis" vectors (1, 0) and (0,1) and see what happens there:

    [tex]\left(\begin{array}{cc}2&3\\0&1\end{array}\right)\left(\begin{array}{cc}1\\0\end{array}\right)= \left(\begin{array}{cc}2\\0\end{array}\right)[/tex]

    [tex]\left(\begin{array}{cc}2&3\\0&1\end{array}\right)\left(\begin{array}{cc}0\\1\end{array}\right)= \left(\begin{array}{cc}3\\1\end{array}\right)[/tex]

    Draw the lines through (0,0) and each of those and imagine them as what the matrix does to the xy-axes. Of course, all points between the xy-axes are changed into points between those lines.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Represent a matrix on the (x,y)-plane
  1. X^y=y^x proof (Replies: 4)

  2. (x^2 - y^2) (Replies: 5)

Loading...