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Linear Transformation and Inner Product Problem

  1. May 15, 2016 #1
    1. The problem statement, all variables and given/known data
    1. Consider the vector space R2 with the standard inner product given by ⟨(a, b), (c, d)⟩ = ac + bd. (This is just the dot product.)

      PLEASE SEE THE ATTACHED PHOTO FOR DETAIlS


    2. Relevant equations
    T(v)=AT*v

    3. The attempt at a solution
    I was able to prove part a. I let v=(v1,v2) and w=(w1,w2)
    apply T(v)=AT*v and do the expansions easily yields the result

    But for part b I am clueless. Please suggest an attempt
     

    Attached Files:

  2. jcsd
  3. May 15, 2016 #2
    Hint: the expression 'standard representation of ##T##' means 'representation of ##T## in an orthonormal basis'.
     
  4. May 15, 2016 #3

    ehild

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    You can choose any pair of independent vectors u and v to find the matrix elements of the transformation T. Let be these two vectors the base vectors of R2, (1,0) and (0,1).
     
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