# Homework Help: Linear Algebra question regarding linear operators and matrix rep. relative to basis

1. Dec 12, 2012

### gothloli

1. The problem statement, all variables and given/known data
Let w = a + bi be a complex number and let T : C -> C be defined by T(z) = w · z.
Considering C as a vector space over R, find the matrix B representing T relative to
the basis {1, i} of C.

2. Relevant equations

3. The attempt at a solution
I think you use eigenvalues and eigenvectors, if T is diagonalizable, but my main problem is finding standard basis of T since z is not defined, hence can you guide me there thanks, please help I have an exam tomorrow!.

2. Dec 12, 2012

### Staff: Mentor

Re: Linear Algebra question regarding linear operators and matrix rep. relative to ba

I don't see that eigenvalues or eigenvectors enter into this at all.
"standard basis of T" makes no sense to me. A basis is associated with a vector space, not a transformation.

You are given a basis for C; namely {1, i}. What is T(1)? What is T(i)?

3. Dec 12, 2012

### gothloli

Re: Linear Algebra question regarding linear operators and matrix rep. relative to ba

sorry I meant to say standard matrix of T not basis. Then can you tell me how to solve the question please, I have an exam tomorrow, I'm so confused, I just need help.

4. Dec 12, 2012

### Dick

Re: Linear Algebra question regarding linear operators and matrix rep. relative to ba

w=a+bi. As Mark44 suggested, if you find T(1) and T(i) then those will be the column vectors of the 2x2 matrix for T in the basis {1,i}. What are they? Express them in terms of the basis.

5. Dec 12, 2012

### gothloli

Re: Linear Algebra question regarding linear operators and matrix rep. relative to ba

okay so I get (a -b)
(b a)

thanks for the help, you made it clear for me.

6. Dec 12, 2012

### gothloli

Re: Linear Algebra question regarding linear operators and matrix rep. relative to ba

I get the matrix (a -b)
(b a)
I don't have time to find the matrix input on this thing.

Thanks for the help, you made it clear

7. Dec 12, 2012

### Dick

Re: Linear Algebra question regarding linear operators and matrix rep. relative to ba

I'm clear you've got it. That's what's important. Don't worry about the notation. I fudge it a lot myself. I'd express that as [[a,-b],[b,a]] and just hope people get it.