Recent content by flyerpower

Thank you, that's the kind of answer i was looking for :)

Why is the inner product of two orthogonal vectors always zero? For example, in the real vector space R^n, the inner product is defined as ||a|| * ||b|| * cos(theta), and if they are orthogonal, cos(theta) is zero. I can understand that, but how does this extend to any euclidean space?

I'm having some troubles understanding the concepts of quotient algebra. May someone explain me what exactly they are, giving some concrete examples? I know that a quotient set is the set of all equivalence classes, but it sounds very vague for me and i can't make the analogy with quotient...

You're right. I was confused because i thought f and f[sub k] are not the same functions. Now it makes sense, thank you.

I don't understand why V is the set of all functions such that f(x)=0 for a finite number of S. For example if S={1,2}, does that mean that a vector in S is (f(1),f(2))? with f(1)=0, f(2)=b, with b in F. Or f(1)=a, f(2)=b, with a,b in F. The basis is {(f[sub 1](1),f[sub 1](2)),f[sub...

Ok, thank you, i'll take one more ride :).

Well, the definition of V doesn't change the situation, the problem is that i don't know the dimension of V, is it finite?

This is what concerned me too. Honestly i don't quite understand the definition of V as it doesn't say anything clear about x in f(x), but, actually i think V is defined such that f(x)=0 for a finite number of elements in S.

It's not specified, so i guess it's f(x) = 0 for all x in S.

Homework Statement Let S be any non-empty set, F be a field and V={ f : S -> F such that f(x) = 0 } be a vector space over F. Let f[sub k] (x) : S -> F such that f[sub k] (x) = 1 for k=x, otherwise f[sub k] (x) = 0. Prove that the set { f [sub k] } with k from S is a basis for the vector space...

Ok, thank you, it's not yet fully clear for me, but I'm starting to get some intuition, i'll do more research :). Thanks again.

Ok, so it is described in terms of photons/unit time/area, that would be something called irradiance, right? And one more question about light, i can't make the intuition of what the frequency and weavelength of an EM wave mean. Well i know they represent variations in electric and magnetic...

This is my question actually, what is the physical meaning of that weakness? by what physical concept is it described?

Suppose a spaceship is at 1 light year distance by Earth and it sends a message back home through an electromagnetic wave, we choose a frequency so that the wave will be a radio wave which requires little energy to produce. How do i know if the wave will reach the Earth? and what characteristics...

The piston is frictionless. And that's pretty much what i said in the second part: p2=p1+mg/S where mg/S is due to the piston's mass. But i cannot find the ratio V1'/V2' from my calculations. I would really apprecied if you checked them. Thanks.