# Linear Transformation and Inner Product Problem

1. May 15, 2016

### i_hate_math

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

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2. May 15, 2016

### geoffrey159

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

3. May 15, 2016

### ehild

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).