1. Limited time only! Sign up for a free 30min personal 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!

Matrix of linear transformation

  1. Apr 1, 2010 #1
    1. The problem statement, all variables and given/known dataFind the matrix of the transformation:

    [tex]T: R^{2} \rightarrow R^{2x2}[/tex]

    [tex]
    \[
    T(a,b) =
    \left[ {\begin{array}{cc}
    a & 0 \\
    0 & b \\
    \end{array} } \right]
    \][/tex]



    2. Relevant equations



    3. The attempt at a solution
    I choose the standard bases for [tex]R^{2}[/tex] and [tex]R^{2x2}[/tex] and call them b and b' respectively.

    [tex]T(1,0) = 1e_{1} + 0e_{2} + 0e_{3} + 0e_{4}[/tex]
    [tex]T(0,1) = 0e_{1} + 0e_{2} + 0e_{3} + 1e_{4}[/tex]

    This gives me a matrix of

    [tex]
    \[
    \left[ {\begin{array}{cc}
    1 & 0 \\
    0 & 0 \\
    0 & 0 \\
    0 & 1 \\
    \end{array} } \right]
    \][/tex]

    However, this doesn't work when I multiply by the column vector (a,b). I get a column vector of (a, 0, 0, b) instead of a 2x2 matrix. What's going on?
     
  2. jcsd
  3. Apr 1, 2010 #2

    radou

    User Avatar
    Homework Helper

    If your R^2x2 is the subspace of all 4x4 matrices of this given form, what is its dimension? You have too many basis vectors here.
     
  4. Apr 1, 2010 #3
    R^2x2 is the space of all 2x2 matrices. It has 4 basis vectors with 1 in the i,j position and zeroes everywhere else.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Matrix of linear transformation
Loading...