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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- anonymous

- katieb

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- anonymous

please elaborate

- anonymous

what u mean elaborate?

- anonymous

"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?

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## More answers

- anonymous

ok

- anonymous

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

- anonymous

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.

- anonymous

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.

- anonymous

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

- anonymous

so you have to prove all ten?

- anonymous

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

- anonymous

:(

- anonymous

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

- anonymous

i made this class honor,, and now im dying

- anonymous

oh wow.... well thanks for trying tho

- anonymous

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

- anonymous

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

- anonymous

what do u mean storm?

- anonymous

i mean its too high level

- anonymous

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

- anonymous

yes

- anonymous

its a cool, site isnt it

- anonymous

yes... what is this site about?

- 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?

- anonymous

the clousures

- anonymous

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

- anonymous

that site is about asking hard question in maths

- 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?

- anonymous

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

- mathmate

How is the tangent space defined?

- anonymous

i defined them above

- 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?

- anonymous

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

- mathmate

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

- mathmate

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

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