Subspaces Definition and 317 Threads

So the parametric equations of a hypersurface in V[SIZE="3"]N are x^1=acos(u^1) x^2=asin(u^1)cos(u^2) x^3=asin(u^1)sin(u^2)cos(u^3) ... x^(N-1)=asin(u^1)sin(u^2)sin(u^3)...sin(u^(N-2))cos(u^(N-1)) x^N=asin(u^1)sin(u^2)sin(u^3)...sin(u^(N-2))sin(u^(N-1)) where a is a constant. How do...

Hey, I have no problems dealing with vectors in space, R^3. But I am having a lot of trouble with vectors in R^n. One of my basic questions is what is R^n. I mean doesn't the vector space already encompass everything? How do I visualize R^n vectors? Can you reccomend any good online tutorials...

see attached equation thank you!

Hi, I'm wondering how I would decide how many "subspaces of each dimension Z_2^3 has." The answer is: 1 subspace with dim = 0, 7 with dim = 1, 7 with dim = 2, 1 with dim = 3. I'm looking for subsets of Z_2^3 which are closed under addition and scalar multiplication. An arbitrary vector in...

Vector Spaces, Subspaces, Bases etc... :( Hello. I was doing some homework questions out of the textbook and i came across a question which is difficult to understand, could somebody please help me out with it? -- if U and W are subspaces of V, define their intersection U ∩ W as follows...

Hello... I've been doing some home work on Vector Spaces and Vector Subspaces and I need help solving a problem... Can somebody please help me? Consider the differential equation f'' + 5f' + 6f' = 0 Show that the set of all solutions of this equation is a vector subspace of the...

Yet another problem I need to get some starting help on: Show that the set of continuous functions f=f(x) on [a,b] such that \int \limits_a^b f(x) dx=0 is a subspace of C[a,b] Thank you

Hi can someone please help me with the following question. Such questions always trouble me because I don't know where to start and/or cannot continue after starting. Q. Let H and K be subspaces of a vector space V. Prove that the intersection of K and H is a subspace of V. By the way...

I have 2 subspaces U and V of R^3 which U = {(a1, a2, a3) in R^3: a1 = 3(a2) and a3 = -a2} V = {(a1, a2, a3) in R^3: a1 - 4(a2) - a3 = 0} I used the information in U and substituted it into the equation in V and I got 0 = 0. So, does it mean that the intersection of U and V is the whole...

How do separation axioms carry over to subspaces? Some are clear -- it's easy to see that if any two points of a space X are separated by neighborhoods, then the same must be true of any subset S of X. But what about the nicer ones? Is it true that if S is a subset of a normal space, that...

Hi everyone- any help would be great! For each integer n>= 2, there exists a vector space V and a linear operator T : L(V ) such that V has exactly n T- invariant subspaces. I think it is true but i do not know how to prove it... awesome thanks!

Having some difficult with general concepts of metric spaces: 1) What is the difference between a subset and a subspace. let's say we have metric space X. and A is a set in that space. Is A necessarily a metric space itself? 2) Why is the metric of X ( d(x,y) for x,y belonging to X )...

I had a question regarding subspaces. Given vectors (a,b,c,d) s.t. \left{\mid}\begin{array}{cc}a&b\\c&d\end{array}\right{\mid}=0 a supspace of \Re^4? Though i kno the answer is yes, but i don't understand like it looks to me that it uses one of the three properties of subspaces; the zero...

Does every linear operator have a nontrivial invariant subspace? My professor mentioned this question in class, but never actually answered it. I am curious if this is true or not and why.

I have to prove or give a counter example to the statement if U1, U2, W are subspaces of V such that V=U1 direct sum W and V=U2 direct sum W, then U2=U1. This is what I did: Let v be an element of V. Then v=v1+v2 for v1 an element of U1 and v2 and element of W and v=v3+v2 for v3 an...

I hope someone can help me (guide) in this theorem. How can I show that a "subset W of a vector space V is indeed a subspace of V if and only if given u and v as vectors in W and a and b are said to be scalars, then au + bv is in W."? Can I assume a vector with my desired number of...

I can't solve a problem about subspaces. Help would be great! U and V are subspaces in the vector space R^4[x] given with: U={p(x)=a0+a1*x+a2*x^2+a3*x^3+a4*x^4; a1+a2+a3+a4=0, a1+a2+2a3+2a4=0, a0+a1=a3+a4} V=L{x^3-x^2+x, x^4+1} Find the dimensions and basis for U, U+V and U?V. Is...