## anilorap 3 years ago need help with heavy stuff. I am defining the derivative as a linear transformation between tangent spaces. so im defining tangent spaces which i need to prove the ten axioms.. need help please

1. Stom

2. anilorap

what u mean elaborate?

3. Stom

"I am defining the derivative as a linear transformation between tangent spaces. so im defining tangent spaces which i need to prove the ten axioms" does it make any sense to you?

4. anilorap

ok

5. anilorap

tangent space as a set of linear approximation of all tangent vectors

6. anilorap

tangent vector can be defined at a point in a vector space, as a order of n-tuples v_p= 〖{a_(1,)…,a_(n,)}〗_p in which exist a parameterized curve c:I→R^n which derivative at 0 have the property c(0)=p and c^' (0)=v_p=〖{a_(1,)…,a_(n,)}〗_p.

7. anilorap

Because in the world of tangent spaces we are working with the properties of vector spaces, vectors in the tangent spaces must satisfy the two operations: i) Vector addition. ii) Scalar multiplication and 10 axioms.

8. anilorap

the first one, i need to prove that when i take two vector spaces in a tangent space and i add them, their sum must be also in the tangent space

9. lawnphysics

so you have to prove all ten?

10. anilorap

yea **crying** i have the idea... but no the knowledge

11. anilorap

:(

12. anilorap

oh wow.. imagine my level.. i am not even in a four year school

13. anilorap

i made this class honor,, and now im dying

14. anilorap

oh wow.... well thanks for trying tho

15. Stom

cooal stuff there, if only i had no reason to celebrate life would i go to wikipedia and sit for the next 2 hours to grasp what tangent spaces are and answer your question

16. Stom

but that certainly is not the case so sorry , http://maths.stackexchange.com/

17. anilorap

what do u mean storm?

18. Stom

i mean its too high level

19. Stom

PS did u check that site PSS my name is stom, without any r

20. anilorap

yes

21. Stom

its a cool, site isnt it

22. anilorap

yes... what is this site about?

23. mathmate

I thought there are only 8 axioms to verify a vector space, four for addition and four for multiplication. Can you tell me the two others?

24. anilorap

the clousures

25. anilorap

if u and v are in W then u + v is in W if u is in W and k is any scalar then ku is in W

26. Stom

27. mathmate

So you must have worked on other vector spaces before, have you started on the axioms yet? Which one(s) do you have problems with?

28. anilorap

i didnt start yet.. i dont know how... because they are not vector spaces anymore,,, they are tangent spaces

29. mathmate

How is the tangent space defined?

30. anilorap

i defined them above

31. mathmate

Can you give examples of some vectors as per the definition? Does the zero vector exist? Does the negative vector exist? Is the zero vector in the space?

32. anilorap

oh wow those are the axioms....if i could give u examples i will be able to prove

33. mathmate

How do you define the tangent vectors, by directional derivatives?

34. mathmate

I suggest you repost as: "linear transformation between tangent spaces" and perhaps someone else can better spot your post.