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Homework Help: 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.

    2. Relevant equations
    Here is some of the preceding material:

    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


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    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
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