You are not logged in.
#1 2012-11-13 06:34:42
- princess snowwhite
- Member
Offline
linear transformation
let V be a real n-dimensional vector space and let T:V-->V be a LT saisfying T(v)= - v for all v belongs to V.
1. show n is even
2.use T to make V into a cmplex vector space such that the multiplication by complex numbers extends the multiplications by real numbers
3. show that with respect to complex vector space structure on V obtained in 2. , T is a complex linear transformation
#2 2012-11-14 00:25:09
- scientia
- Full Member
Offline
Re: linear transformation
princess snowwhite wrote:
let V be a real n-dimensional vector space and let T:V-->V be a LT saisfying T(v)= - v for all v belongs to V.
1. show n is even
Have you left something out? This statement does not follow from just what you have stated.
PS: I found your mistake. You want T2(v)= −v for all v ∈ V.
Last edited by scientia (2012-11-14 00:33:24)
#3 2012-11-14 04:40:53
- princess snowwhite
- Member
Offline
Re: linear transformation
I have no idea about the answer. But the question is correct.
#4 2012-11-14 07:34:29
- scientia
- Full Member
Offline
Re: linear transformation
I don't think your question is correct. 
Last edited by scientia (2012-11-14 07:37:55)
#5 2012-11-15 16:59:29
- princess snowwhite
- Member
Offline
Re: linear transformation
Ops! Sorry........ Yes I wanted T2(v)= −v