Am I understanding this right? (linear algebra and discrete math)

[Mucman]

I think I finally understand what a vector space is... can someone please let me know if I got this right...

A vector [x1,x2] in R2 is analagous to
A vector [x1,x2] is in the vector space that is spanned by two vectors in R2

is that right? So is a vector space a space that is a span of vectors?
can these be vector spaces?

sp([2,4]) a vector in this vector space could be [4,8]?

As for discrete math, I would like to know if I am understanding big-O notation (girls don't get excited )

if f(x) = x^3 + x + 1 is O(x^3)

that means f(x) will be bounded below by x^3 for some value of C where Cx^3 is always more than f(x) for some x > i ?

another example is x^3 is not O(x^2), right?

if someone has a good way of explaining it, I would love to hear it

 

[AngelOfDeath]

<< A vector [x1,x2] in R2 is analagous to A vector [x1,x2] is in the vector space that is spanned by two vectors in R2 >>

Yes that's correct. And yes you can create a vector space from another set of vectors. The vectors in a vectorspace can also create a vectorspace or a sub-space.


<< sp([2,4]) a vector in this vector space could be [4,8]? >>

Yes since it's 2x the vectorspace if I understand your question right.

AoD

 

[Mucman]

so a subspace of a vector space is antoher vector space but it doesn't span the original vector space?

I did big-O in another course that isn't affiliated with linear algebra... so you don't need to explain it in vectors.

thanks for the reply... I feel a little more confident about it now. Now to start cracking on those generating functions

 

[GL]

Mucman,

Just browsed through the other guy's response for the algebra part and it seems alright. As for the Big-&quot;Oh&quot; notation, it's very easy to understand. Big-&quot;Oh&quot; is the worst case scenario in terms of time complexity. Later on, you'll lean about Big-&quot;theta&quot; and some other bounds for time complexity but Big-&quot;Oh&quot; is by far, the most intuitive in my opinion.

If you have x^3 + x^2 + x, you will have a time complexity of the highest degree element of the polynomial - that is O(x^3). The reason being that as x approaches infinity, the term x^3 dwarfs (x^2 + x) - in other words, the remaining terms become insignificant. So, just always look for the highest degree term and that's your big-Oh time complexity. Hopefully someone else will confirm this though just to ensure it is always the case that big-Oh time complexity is the highest degree term (by the way...I don't believe you include the coefficient in from of the highest degree term either because that becomes insignificant as x approaches infinity).

-GL

 

[AngelOfDeath]

Here by confimred. When u explained the O-notation I could remember it .

Damn, it's 3 years since I had this.

AoD

 

[AngelOfDeath]

<< so a subspace of a vector space is antoher vector space but it doesn't span the original vector space? >>

Not neccesarily, since you may have a subspace of vectors spanning the original vectorspace. But ofcourse in most cases yes.

AoD

 

[Mucman]

Thanks guys! I have seen big-theta and big-omega (I think), but we really don't need to know them. We were doing sorting algorithms and it was said to be O(xlog(x)). If we are in the context of time for algorithms that is much better than O(x^2), but not as good as O(x)? I think I understand it now... I am just wondering what kind of question is going to be on the final about that stuff.

AoD, so you are saying that the subspace of a vector space is a subset (not necessarily (sp?) a proper subset) of the vector space then?

 

[AngelOfDeath]

<< the subspace of a vector space is a subset (not necessarily (sp?) a proper subset) of the vector space then? >>

Yes that's right .

AoD

 

[Mucman]

sweet

This semester might end up being really good