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

princess snowwhite
Member
Registered: 2012-11-06
Posts: 29

### 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

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

scientia
Member
Registered: 2009-11-13
Posts: 224

### 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 T[sup]2[/sup](v)= −v for all vV.

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

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

princess snowwhite
Member
Registered: 2012-11-06
Posts: 29

### Re: linear transformation

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

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

scientia
Member
Registered: 2009-11-13
Posts: 224

### Re: linear transformation

I don't think your question is correct.

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

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

princess snowwhite
Member
Registered: 2012-11-06
Posts: 29

### Re: linear transformation

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

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