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Linear Algebra question regarding linear operators and matrix rep. relative to basis 
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#1
Dec1212, 07:33 PM

P: 30

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
Dec1212, 08:07 PM

Mentor
P: 21,216

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


#3
Dec1212, 08:25 PM

P: 30

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
Dec1212, 09:15 PM

Sci Advisor
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Thanks
P: 25,251

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



#5
Dec1212, 10:41 PM

P: 30

(b a) thanks for the help, you made it clear for me. 


#6
Dec1212, 10:42 PM

P: 30

(b a) I don't have time to find the matrix input on this thing. Thanks for the help, you made it clear 


#7
Dec1212, 10:50 PM

Sci Advisor
HW Helper
Thanks
P: 25,251




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