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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

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  1. Stom
    • 3 years ago
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    please elaborate

  2. anilorap
    • 3 years ago
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    what u mean elaborate?

  3. Stom
    • 3 years ago
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    "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
    • 3 years ago
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    ok

  5. anilorap
    • 3 years ago
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    tangent space as a set of linear approximation of all tangent vectors

  6. anilorap
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    so you have to prove all ten?

  10. anilorap
    • 3 years ago
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    yea **crying** i have the idea... but no the knowledge

  11. anilorap
    • 3 years ago
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    :(

  12. anilorap
    • 3 years ago
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    oh wow.. imagine my level.. i am not even in a four year school

  13. anilorap
    • 3 years ago
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    i made this class honor,, and now im dying

  14. anilorap
    • 3 years ago
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    oh wow.... well thanks for trying tho

  15. Stom
    • 3 years ago
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    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
    • 3 years ago
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    but that certainly is not the case so sorry , http://maths.stackexchange.com/

  17. anilorap
    • 3 years ago
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    what do u mean storm?

  18. Stom
    • 3 years ago
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    i mean its too high level

  19. Stom
    • 3 years ago
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    PS did u check that site PSS my name is stom, without any r

  20. anilorap
    • 3 years ago
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    yes

  21. Stom
    • 3 years ago
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    its a cool, site isnt it

  22. anilorap
    • 3 years ago
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    yes... what is this site about?

  23. mathmate
    • 3 years ago
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    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
    • 3 years ago
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    the clousures

  25. anilorap
    • 3 years ago
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    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
    • 3 years ago
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    that site is about asking hard question in maths

  27. mathmate
    • 3 years ago
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    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
    • 3 years ago
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    i didnt start yet.. i dont know how... because they are not vector spaces anymore,,, they are tangent spaces

  29. mathmate
    • 3 years ago
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    How is the tangent space defined?

  30. anilorap
    • 3 years ago
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    i defined them above

  31. mathmate
    • 3 years ago
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    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
    • 3 years ago
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    oh wow those are the axioms....if i could give u examples i will be able to prove

  33. mathmate
    • 3 years ago
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    How do you define the tangent vectors, by directional derivatives?

  34. mathmate
    • 3 years ago
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    I suggest you repost as: "linear transformation between tangent spaces" and perhaps someone else can better spot your post.

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