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

by gothloli
Tags: algebra, basis, linear, matrix, operators, relative
 P: 31 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!.
Mentor
P: 21,311
 Quote by 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
I don't see that eigenvalues or eigenvectors enter into this at all.
 Quote by gothloli , but my main problem is finding standard basis of T
"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)?
 Quote by gothloli since z is not defined, hence can you guide me there thanks, please help I have an exam tomorrow!.
 P: 31 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.
HW Helper
Thanks
P: 25,228
Linear Algebra question regarding linear operators and matrix rep. relative to basis

 Quote by gothloli 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.
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.
P: 31
 Quote by Dick 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.
okay so I get (a -b)
(b a)

thanks for the help, you made it clear for me.
P: 31
 Quote by Dick 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.
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