Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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 vV.

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