Map Definition and 403 Threads

It's used in a certain proof that I'm reading. A is a linear map from a vectorspace V onto itself. They say they can rewrite the vector space as \mathcal V = \bigoplus_\mu \mathbb C^{m_\mu} \otimes \mathcal V^\mu and I understand this, but they then claim one can (always, as any linear map)...

We were taught both methods to minimize gates. I frankly just want to pick one method all the time and become an expert in it, rather then try them both. So, according to your experience, which method do I better pick?

first i hope is the correct forum to ask this kind of question. so i asked to find the minimum SOP function from the Karnaugh map (given in the picture). so i started to solve it as you can see in the picture. and this what i got:fsop=AB+BC+ACD'X' till here i think is ok. now this is...

Homework Statement Let X and Y be ordered sets in the order topology. I want to show that a function f:X→Y is injective. We are given that f is surjective and preserves order. Homework Equations Definition of an order preserving map: If x≤y implies f(x)≤f(y) The Attempt at a...

Hi, All: I saw this question somewhere else: we are given any two topological spaces (X,T), (X',T'), and we want to see if there is always at least one continuous map between the two. The idea to say yes is this: we only need to find f so that f-1(U)=V , for every U in T', and some V in T. So...

Is there a C^infty map that is one to one from R^n to R? Thanks.

Throughout most of the discussions I have had about science, philosophy, physics, math, and life in general over the past 35 years (since beginning my first undergraduate class in philosophy) there is one element of every discussion that returns. It has to do with the statement "the map is not...

http://www.ted.com/talks/allan_jones_a_map_of_the_brain.html?utm_source=newsletter_weekly_2011-11-11&utm_campaign=newsletter_weekly&utm_medium=email" http://www.ted.com/speakers/allan_jones.html" http://human.brain-map.org/explorer.html" Lots of explore and research here, cheers Paul...

I have a 3D shape described by a triangulation map i.e. a map between the vertices to the faces of the shape which are all triangles. I then sliced the shape by a plane and computed the intersections of the plane and the triangle faces. Each triangle face that intersects the plane, will have...

I live less than a mile from the SAFZ near Frazier Park, and would like to identify related surface features like escarpments, tuff outcrops, etc. After much Googling, I have found no maps that would help me locate the identified fault line locations within even 1000ft. None. Has anyone here...

I have been exploring an algebraic structure with a map (_)* such that (x)*** = (x)* but in general it is not an involution. Also, the set of elements e such that e** = e do not form a substructure because they are not closed to addition. Has anyone seen such maps before, or know/can...

Chemistry: "Road map" question. Borax can be converted to pure boron through the series of chemical reactions shown below: Pure boron is isolated in the final step of this reaction series. The starting material Y, is a non-polar gas with terminal chlorine atoms. Compound Y (2 mol) is heated...

Why, hello there. I'm doing Karnaugh maps. I'm using them to device gates to express the numbers 0, 1, 2, 3, 4 in a seven segmented digital display. Our teacher has provided us with predrawn Karnaugh maps, where we simply fill in the 1's and 0's. However, he's decided to invert the...

Let G have a transitive left action on a set X and set H = G_x to be the stabilizer of any point x. Show that the map defined by f: G/H \rightarrow X where f(gH) = gx is well defined, one to one, and onto. i think i know how to show well defined. letting g1 H = g2 H, if i multiply on the...

Homework Statement Verify that any square matrix is a linear operator when considered as a linear transformation. Homework Equations The Attempt at a Solution If a square matrix A\inℂ^{n,n} is a linear operator on the vector space C^{n}, where n ≥ 1, then the square matrix A is...

I have no programming experience and trying to get mathematica to do what I need it to do is frustrating. I have the following functions that I need to iterate. For notational purposes, k[t+1] is the value of K in the next period. w is a parameter. k[t+1] = -x[t] - y[t] + w x[t+1] =...

Don't know whether this belongs in chemistry or Earth science but there has been discussion about salinity here. http://www.bbc.co.uk/news/science-environment-15033532

Hi: More on Prelims: We have a map f: S^3 -->S^3 ; S^3 is the 3-sphere , given by: (x1,x2,x3,x4)-->(-x2,-x3,-x4,-x1). We're asked to find its degree, and to determine if f is homotopic to the identity. I computed that f^4 ( i.e., fofofof ) is the identity, and we have that...

Hi, Algebraists: The modN reduction map r(N) from a matrix group (any group in which the elements are matrices over Z-integers) over the integers, in which r is defined by r(N) : (a_ij)-->(a_ij mod N) is not always commutative, e.g.: r(6) :Gl(2,Z) --Gl(2,Z/N) is not...

Hi All, I am trying to draw a map, the raw data I have is Speed and G_Force (Lat and Acce). I have attached a XLS of the RAW data I have. Its from a race track, (I had to trim the file to 100kb, so it might or might not loop). I don't have a GPS, but I have seen software draw maps based on...

Homework Statement I have to find a conformal map from \Omega = \{ z \in \mathbb C | -1 < \textrm{Re}(z) < 1 \} to the unit disk D(0,1) Homework Equations an analytical function f is conformal in each point where the derivative is non-vanishing specifically, we can think of linear...

Homework Statement "Show that there is no conformal map from D(0,1) to \mathbb C" and D(0,1) means the (open) unit disk Homework Equations Conformal maps preserve angles The Attempt at a Solution I don't have a clue. I thought the clou might be that D(0,1) has a boundary, and C...

Has anyone ever drawn a gravity map of the Earth? i mean one that looks at mountain ranges, Vallie's, oceans, and shows the gravity (topology), or the shape of the deformation from a perfect sphere. edit, may be this should go in the Earth forum but i think it is more, gp.

Hello, I was wondering if there were alternative definitions to a "function" ( alternative to the standard f is a subset of A X B if f : A -> B ). I was introduced to the "general" definition of a cartesian product ( with respect to an indexing set H ) , it is weird to me because the general...

Novice question :blushing: I've been reading Brian Greene's "The Hidden Reality". It occurred to me that spacetime across the 2D analog of the U could be much like an isometric weather map. Could it be that the U isn't expanding, but that our region, like a High on a weather map is rushing...

Homework Statement Find the Linear Fractional Transformation that maps the line Re\left(z\right) = \frac{1}{2} to the circle |w-4i| = 4. Homework Equations For a transform L\left(z\right), T\left(z\right)=\frac{z-z_{1}}{z-z_{3}}\frac{z_{2}-z_{3}}{z_{2}-z_{1}}...

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 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...

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

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...