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

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

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)*

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

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

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

I don't think your question is correct.

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

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

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

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