Question

Vector spaces...

Answer 1

Is the set C1[1, 6] of all differentiable functions defined on the interval [1, 6], a vector space?

Answer 2

it is if the vector space axioms are satisfied, u have to check them.

Answer 3

Yeah, I know that you check whether the space is closed under addition and all that jazz, but I don't understand how to do that with this notation... Could you give me an example or two? That would really help :S

Answer 4

What does C1[1, 6] mean? (I usually only deal with vector spaces that have proper vectors in them, lol.

Answer 5

Erm I don't know - I was hoping someone could tell me... Presumably just some arbitrary name for the solution set?

Answer 6

sure it is

Answer 7

an excellent way for you to learn the vector space axioms. just check them against your space (functions continuous on [1,66

Answer 8

sorry. continuous on [1,6]

Answer 9

the only one tiny small non trivial piece of the exercise will be to say that if f, g, are continuous on [1,6] then so is
f+g
f-g
af etc,or just say so is af+bg. that is, sum of continuous functions is continuous etc. that is all

Answer 10

ooh i guess i should read. it doesn't say C[1,6] it says C1[1,6] space of functions differentiable on [1,6]
well everything i said above if true if you just replace "continuous" by "differentiable"
guess i should learn how to read, but it is really the same

Answer 11

sum of two differentiable functions is differentiable, etc. just check the axioms one by one to make your teacher happy. they will all work out fine

Answer 12

Ah, I see, C^1 is the space of continuously differentiable functions, C^k if kth-derivative exists and is continuous.

What's in a name, eh?

Answer 13

OK, I have a look, not more posts in this thread...