Are vector-components vectors?

Discuss.

Vector components: magnitude and direction.
Direction is a vector.
Magnitude isn't.

Do your own fucking homework, anyone should know this if they did any maths.

fields are trivial vector spaces over themselves. so yes.

Ok, it was just a tad annoying, cos I've got one book who specifically says it should be considered as vectors, and yet anotherone who says the total opposite.

Magnitude is a scalar,  i know that - but "direction is a vector", true enough.

But can you consider vector-components forces? Technically, they DO have a direction and they certainly have a "length", absolute value or magnitude, whatever you choose to call it. This should make them forces, right? But then you could make vector-components of vector-components and it would all be a total mess...

oh god not more confused high-school level shit. vectors do not have magnitude, in general. what's the distance between "x-1" and "x^3-x+6" (both "vectors")?

fuck off and die plz

to find a magnitude of a vector you will have to fist define an inner product in the vector space :\

>>5
God /sci/ sure has a lot of ignorant fucktards.
Of course vectors have magnitude.
Using (x,y) format, vectors just have a magnitude of SQRT( x^2 + y^2 ).
Even some highschool dipshit should know that.

>>4
Let me try to be a bit nicer about this than that fucktard >>5
Forces can be modelized as vectors. It's incorrect to say to say that the opposite necessarily holds true.

>>7

really? then lets take C^inf[0,pi/2] as a vector space. what's the magnitude of the vector f(x)=sin(x) then? and who the fuck uses "dipshit" these days anyway?

>>8

you can to define norms of functions.
like if you take a vector space of C[0,1] i.e continuous function from closed interval [0,1] to reals, you can take a norm to be for example
d_inf (f) = sup{|f(t)|, t in [0,1]
which induces a metric
d_inf (f,g) = sup{|f(t)-g(t)|, t in [0,1]}

You could also define
d_p (f) = [integral 0 to 1 of |f(x)-g(x)|^p dx]^(1/p)
That will induce a metric on the vector space as well.
in the vector space

^ sorry that's meant to be continuous functions from [0,1]

>>8
You have been Owned by
>>9
>>10
and
>>7

Congratu-fucking-lations.

fuck yo couch nigga!

>>11

I am not sure it's possible to define an inner product in every vector space though.

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