Question

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

Answer 1

please elaborate

Answer 2

what u mean elaborate?

Answer 3

"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?

Answer 4

ok

Answer 5

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

Answer 6

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.

Answer 7

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.

Answer 8

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

Answer 9

so you have to prove all ten?

Answer 10

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

Answer 11

:(

Answer 12

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

Answer 13

i made this class honor,, and now im dying

Answer 14

oh wow.... well thanks for trying tho

Answer 15

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

Answer 16

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

Answer 17

what do u mean storm?

Answer 18

i mean its too high level

Answer 19

PS
did u check that site

PSS my name is stom, without any r

Answer 20

yes

Answer 21

its a cool, site isnt it

Answer 22

yes... what is this site about?

Answer 23

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?

Answer 24

the clousures

Answer 25

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

Answer 26

that site is about asking hard question in maths

Answer 27

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?

Answer 28

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

Answer 29

How is the tangent space defined?

Answer 30

i defined them above

Answer 31

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?

Answer 32

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

Answer 33

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

Answer 34

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