Map Definition and 441 Threads

If I'm correct Planck will publish its all-sky CMB map (foreground deducted) this year. What's to be expected from this? Is another revolution coming?

Hi, I am trying to understand the concept of tangent map and following the ebook of S S Chern. I am a bit confused about the derivation of the tangent map acting on the basis I tried for sometime to type out the equation but it appears I am having problems with the display and not sure what is...

Homework Statement Let F be a finite field of characteristic p. As such, it is a finite dimensional vector space over Z_p. (a) Prove that the Frobenius morphism T : F -> F, T(a) = a^p is a linear map over Z_p. (b) Prove that the geometric multiplicity of 1 as an eigenvalue of T is 1. (c) Let F...

Suppose you're looking at a complex vector space X, and you know that, for some x in X, you have f(x) = 0 for every linear map on X. Can you conclude that x = 0? If so, how? This seems easy, but I can't think of it for some reason. (EDIT: Assume it holds for every CONTINUOUS (i.e...

Homework Statement Prove a proper continuous function from R to R is closed. Homework Equations proper functions have compact images corresponding to compact preimages, continuous functions have open images corresponding to open preimages, in R compact sets are closed and bounded...

Homework Statement Hi, i need to show if the map D: Vn maps Vn for f(x) maps to f '(x) is diagonalizable. I know how to do this with matrices i am given, but i don't know how to write D as a matrix. Homework Equations The Attempt at a Solution I'd really appreciate it if someone...

Here is theorem 9.2 from Stephen Willard's General Topology: If X and Y are topological spaces and f:X\to Y is continuous and either open or closed, then the topology \tau on Y is the quotient topology induced by f. So f has to be onto doesn't it? Otherwise there will be multiple...

Homework Statement Could someone define the notion of an integral for a map, x → g(x), x element of R2 or xn+1=g(xn thanks

I was glad to see this paper for several reasons. The volume operator in Loop Gravity is the locus of some interesting unresolved questions. The kind that requires and attracts creative mathematicians IMHO. This first paper from Gene Bianchi and Hal Haggard is just a 4-page letter I guess for...

I've been thinking about the following question: if x\in R^n and y=Cx\in R^p where matrix C describes the linear map from n dimensional reals to p dimensional reals. If we only have access to y and want to recover the information about x, which components in x are needed? I kind of figured out...

Determine if the canonical map Z to Zsubscript5 is 1-1 and onto. Prove your answer Im not sure how to prove it but I am almost positive that its onto and not 1-1. I believe it onto because Z contains all the integers and Zsubscript5 contain the equivalence classes [0] [1] [2] [3] [4]. I...

Is this statement true or false if false a counterexample is needed if true then an explanation If T : U \rightarrow V is a linear map, then Rank(T) \leq (dim(U) + dim(V ))/2

In Sean Carroll's GR book I found the following statement: there is no simple map between classical and quantum theories, - there are classical theories with no quantum counterpart - classical theories with multiple quantum versions - quantum theories without any classical analogue Could...

Ok I'm not sure if this question belongs here, but I am learning this in a CS class and the people at math.stack wouldn't know about this stuff, so here it goes. I'm having a hard time understanding how to find the don't-care values in a Kmap. What does it even mean? If I have a boolean...

Homework Statement The scale on a map is 1:25000. The length of a wall on the map is 3.2 mm. Find the actual length in metres.Homework Equations The Attempt at a Solution

Can a function be defined such that for a complex argument z = x + iy, the function will uniquely map z onto the real number line? I have a hunch that this would not be possible, but if such a function existed, it could be used to define a unique ordering of the complex numbers without the need...

Homework Statement Let V and W be vector spaces and let f:V\rightarrow W be a linear map. Show that f is a tensor of type (1,1) Can someone please show how to do this , I have no idea how to do it. Homework Equations The Attempt at a Solution

Hi! I need to write MATLAB script, which will be plotting corretation function for two-dimmensial system. Henon map is not my system, but is very popular, so solusion for henon map can be very helpful for me. Have anybody know code for have plot like this...

Homework Statement I need a example of a continuous function f:(X, d) -> Y(Y, p) does NOT map a Cauchy sequence [xn in X] to a Cauchy sequence of its images [f(xn) in Y] in the complex plane between metric spaces. Homework Equations If a function f is continuous in metric space (X, d), then...

Let X and Y be topological spaces; let p:X -> Y be a surjective map. The map p is said to be a quotient map provided a subset U of Y is open in Y if and only if p^-1(U) is open in X. Let X be the subspace [0,1] U [2,3] of R, and let Y be the subspace [0,2] of R. The map p:X -> Y defined by...

Homework Statement This problem is a bit of a digression (at least it seems so) from the problems about imbeddings I'm dealing with currently (and I yet have a few more to complete). Let X and Y be spaces. Define e : X x C(X, Y) --> Y with e(x, f) = f(x). e is called the evaluation map...

I was wondering how someone would go about charting stars on their own, pencil and paper style. Particularly, I was curious how astronomers charted the positions of stars and paths of planets hundreds of years ago, and was hoping to replicate this. I understand it's probably very involved, but...

I was checking out a developing blizzard forecast for the northeast US today when I saw this interesting fog feature over the South Dakota, Nebraska, Oklahoma area. http://www.weather.com/maps/maptype/currentweatherusnational/uscurrentweather_large.html EDIT: The image is changing. It was the...

Homework Statement exp^\prime(0)B=B for all n by n matrices B. Homework Equations exp(A)= \sum_{k=0}^\infty A^k/k! The Attempt at a Solution Obviously I want to calculate the limit of some series, but I don't know what series to calculate. I wanted to try \lim_{h \to...

Hi all. I am doing a programming project where I have a map which is 879x436 pixels. At all endpoints I have the geographical coordinates in latitude and longitude corresponding to 0x0, 0x436, 879x0 and 879x436 pixels endpoints X/Y in all corners. My biggest problem is how to calculate the...

I'm having trouble seeing why the following is true: let M be a simply connected manifold and s a smooth map from M to U(1). Then why does it follow that s = e^(iu) for some smooth function u from M to R? Thanks!

Homework Statement Here's a nice one. I hope it's correct. Let p : X --> Y be a closed, continuous and surjective map such that p^-1({y}) is compact for every y in Y. If X is Hausdorff, so is Y. The Attempt at a Solution Let y1 and y2 in Y. p^-1({y1}) are then p^-1({y2}) disjoint...

Homework Statement Let p : X --> Y be a closed, continuous and surjective map. Show that if X is normal, so is Y. The Attempt at a Solution I used the following lemma: X is normal iff given a closed set A and open set U containing A, there is an open set V containing A and whose...

I often look up at the sky and wonder how far away this or that star/object is. I know that most discernible stars are in our neighborhood, but I have a hard time figuring out just how close they are. Is there a map/graphic that would map all the objects we can see with a naked eye in our...

Homework Statement I have posted this problem on another website (mathhelpforum) but have received no replies. I don't know whether this is because no one knows what I am talking about or if it's just that no one can find a fault with my reasoning. Please please please could you post a reply...

http://blogs.nationalgeographic.com/blogs/news/breakingorbit/2010/11/new-dark-matter-map-hubble.html?source=link_tw20101112hubble" i found this article interesting , so shared here

Make a circuit to multiply two 2-bit numbers AB and CD together to produce a 4-bit output. (a) construct a truth table to represent all states of the inputs and the corresponding outputs. (b) make a Karnaugh map for each output bit. Write down the Boolean algebraic expressions that describe...

I don not know whether I was right or not, please give me a hint. (R3,+) can be considered a Lie group. and its TG in 0 is still R3. suppose X as a infinitesimal generater, it can give a left-invariant vector field and also an one-parameter subgroup. but i think, this one-parameter...

I want a projection of Earth where distances are undistorted. i.e. 10 degrees of latitude at the equator is exactly the same map distance as 10 degrees of latitude at the Arctic Circle. As a disqualified example, the Mercator Projection has map distance increasing with increasing latitude...

urgent homomophim and cannoical map assignement due in 13 hours due now

Homework Statement Let V={a cosx + b sinx | a,b \in R} (a) Show that V is a subspace of the R-vector space of all maps from R to R. (b) Show that V is isomorphic to R^2, under the map f: V\rightarrowR^2 a cosx + b sinx \rightleftharpoons [ a over b ] (this is...

Homework Statement Let f:V\rightarrow V be a linear map and let v\inV be such that f^n(v)\neq0 and f^(n+1)(v)=0. Show that v,f(v),...,f^(n-1)(v) are linearly independent. The Attempt at a Solution I'm really stuck with this one. I know the definition of linear independence and...

Homework Statement the question here said is L, linear transformation/mapping is singular? i'm still googling the definition singular linear map, can anyone give me the definition please T_T p/s; i thought it L maybe the matrix representation, but the question L : R^m -> R^n...

Now F:S^2->R^4 is a map of the following form: F(x,y)=(x^2-y^2,xy,xz,yz) now using the smooth covering map p:S^2->RP^2, p is the composition of inclusion map i:S^2->R^3 and the quotient map q:R^3\{0}->RP^2. show that F descends to a smooth embedding of RP^2 into R^4. Is the problem asked to...

Suppose M and N are smooth manifold with M connected, and F:M->N is a smooth map and its pushforward is zero map for each p in M. Show that F is a constant map. I just remember from topology, the only continuous functions from connected space to {0,1} are constant functions. With this be...

Homework Statement Let T: \mathbb{R}^3 \to \mathbb{R}^3 be the linear map represented by the matrix \begin{pmatrix} 4 & -1 & 0 \\ 6& 3 & -2\\ 12& 6 & -4\end{pmatrix} What is the image under T of the plane 2x - 5y + 2z = -5? Homework Equations None The Attempt at a Solution I...

Vector Help! Homework Statement The treasure map in the figure gives the following directions to the buried treasure: "Start at the old oak tree, walk due north for 490 paces, then due east for 150 paces. Dig." But when you arrive, you find an angry dragon just north of the tree. To avoid the...

Homework Statement Let F be the set of all functions f mapping R into R that have derivatives of all orders. Determine whether p is an isomorphism of the first binary structure with the second. 1. <F, +> with <R, +> where p(f) = f'(0) 2. <F, +> with <F, +> where p(f)(x) = \int^{x}_{0}...

In all map, we always see the north on top, why's that? when was this way first used? Anybody know? Thanks

Homework Statement T(2,1)---> (5,2) and T(1,2)--->(7,10) is a linear map on R^2. Determine the matrix T with respect to the basis B= {(3,3),(1,-1)} Homework Equations The Attempt at a Solution matrix = 5 7 2 10 ?

The terms "function" and "map". I have noticed that the term "map" is used more often than "function" when a map/function is defined using the "mapsto" arrow, as in "the map x\mapsto x^2 ". It has occurred to me that when a function is defined this way, it's usually not clear what the codomain...

Why do Karnaugh map work? I don't understand how they work. If I follow the rules I get a minimized expression easily enough...it just seems like magic.

I'm trying to show an inverse map composed with its noninverse results in the identity in terms of the set map f:X-->Y between topological spaces when f is one to one function. If I define the inverse map of a set as the disjoint union of the inverse map of each point in the set in Y, then...

It's easy to construct maps of even degree from the three-sphere to real projective three-space. Do there exist maps of odd degree?

it is easy to construct a map from S^2 to S^2, with covering time being unity but how to do the similar task on the projected manifold RP^2=S^2/Z_2? i tried to use the stereographical trick the points on the lower half semisphere are projected onto the plane the problem is that the...