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!

Matrix of a Linear Transformation Example

  1. Dec 4, 2015 #1
    1. The problem statement, all variables and given/known data
    Hi this isn't really a question but moreso understanding an example that was given to me that I not know how it came to it's conclusion. This is a question pertaining linear transformation for coordinate isomorphism between basis.
    https://imgur.com/a/UwuAC


    2. Relevant equations
    Here is some of the preceding material:
    https://imgur.com/a/acpyU

    3. The attempt at a solution
    I'm not sure how it came to it's conclusion for the basis G, for example the vector [1,0,0] doesn't yield the same result as the standard basis, but gets [1,-2,2] instead even though it is a standard basis e1. I thought for [1,1,0] in G the result would be [1,1,2] but instead it's [-1,1,0]. I've tried working backwards from the solution but that hasn't helped. Can anyone help me understand this?
     
  2. jcsd
  3. Dec 5, 2015 #2

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    First thing, do you know how to compute the matrix representing ##C_G##?

    Once you have the matrix for ##C_G##, you can compute (for example) ##C_G(T(1))=C_G\begin{pmatrix}1\\0\\2 \end{pmatrix}## and see why it "doesn't yield the same result as the standard basis".
     
    Last edited: Dec 5, 2015
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Matrix of a Linear Transformation Example
Loading...