• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Linear Transformation and Inner Product Problem

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
 

Attachments

Hint: the expression 'standard representation of ##T##' means 'representation of ##T## in an orthonormal basis'.
 

ehild

Homework Helper
15,314
1,739
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).
 

Want to reply to this thread?

"Linear Transformation and Inner Product Problem" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top