linear transformation

princess snowwhite · 2012-11-12 07:34:42

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

scientia · 2012-11-13 01:25:09

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 T[sup]2[/sup](v)= −v for all v ∈ V.

Last edited by scientia (2012-11-13 01:33:24)

princess snowwhite · 2012-11-13 05:40:53

I have no idea about the answer. But the question is correct.

scientia · 2012-11-13 08:34:29

I don't think your question is correct.

Last edited by scientia (2012-11-13 08:37:55)

princess snowwhite · 2012-11-14 17:59:29

Ops! Sorry........ Yes I wanted T2(v)= −v

Math Is Fun Forum

#1 2012-11-12 07:34:42

linear transformation

#2 2012-11-13 01:25:09

Re: linear transformation

#3 2012-11-13 05:40:53

Re: linear transformation

#4 2012-11-13 08:34:29

Re: linear transformation

#5 2012-11-14 17:59:29

Re: linear transformation

Board footer