Map Definition and 403 Threads

Hello, I just cracked open this abstract algebra book, and saw a problem I have no idea how to solve. Instruction: Determine whether the given map \phi is an isomorphism of the first binary structure with the second. If it is not an isomorphism, why not? (Note: F is the set of all functions...

I am trying to read through this paper on the standard model. The ideas seem straightforward enough, but as always, I'm tripping over the "physicist's math" it uses. I was wondering if I can get some clarification or general guidance...

Hi there, I am trying to plot the coordinates of Supernovae onto what I think is known as a hammer plot i.e a 2D plot representing the surface of a sphere. I have no idea how to do this, and have been searching the internet to no avail. Can anyone offer any advice ? I only have a basic...

Homework Statement Let V and W be vector spaces over F, and let T: V -> W be a surjective (onto) linear map. Suppose that {v1, ..., v_m, u1, ... , u_n} is a basis for V such that ker(T) = span({u1, ... , u_n}). Show that {T(v1), ... , T(v_m)} is a basis for W. Homework Equations Basic...

Im not sure if this is the right section to post this question.. Calculate the differential of the map f:R^3 -> R^2 , (x ,y ,z)->(xy3 + x2z , x3y2z) at (1 ,2 ,3) in the direction (1 ,-1 , 4) I know how to get the differential of the map (finding the jacobian matrix) but the only part i am...

Homework Statement For each of the following pairs of vectors, define an explicit isomorphism to establish that the spaces are isomorphic. Prove that your map is an isomorphism. a)P3 and R4 b)P5 and M(2,3) Homework Equations None The Attempt at a Solution a)I know that P3 and R4...

Hi. I'm trying to find the degree of the map of f(g,h)=g.h (i.e. multiplication in g) for fixed g. It is a map G-->G (if we fix g). We can assign a degree to this map for any topological group for which the last non-zero homology group is Z and proceed like we do for the degree of a map...

Homework Statement Consider the map phi : C -> I which maps each point of the middle third Cantor set C, considered as a subset of real numbers between 0 and 1 written in base 3 and containing only digits 0 and 2, to the set of real numbers I=[0,1] written in base 2, according to the rule...

if you are given a contour map how could you calculate the volume of the hill.

Hello all, I am trying to solve this exercise here: Let \phi denote the Frobenius map x |-> x^p on the finite field F_{p^n}. Determine the Jordan canonical form (over a field containing all the eigenvalues) for \phi considered as an F_p-linear transformation of the n-dimensional F_p-vector...

Homework Statement Let D* be the parallelogram with vertices at (-1,3), (0,0), (2,-1), and (1,2), and let D be the rectangle D = [0,1] X [0,1]. Find a T such that D is the image set of D8 under T. Homework Equations Not much to say other than T(D*) = D The Attempt at a Solution...

If i were to say: Map vector A onto line l would that mean the projection of A onto l or the rotation of A onto l?

Homework Statement Let H, K be subgroups of a finite group G. Consider the map, f : H \times K \rightarrow HK : (h,k)\rightarrow hk. Describe f^{-1}(hk) in terms of h, k and the elements of H\cap K. Homework Equations HK = \{hk : h \in H, k \in K \} f^{-1}(hk)=\{ (h',k') : f(h',k')=hk...

Homework Statement Consider the map F: C0([a,b],Rn) --> R, F(\phi)=\int\phi(t)\phi(t)dt (This is the integral from a to b). Write F as a composition of three maps, each of which is linear or bilinear. Then use the chain rule and generalized product rule to compute DF(\phi). Homework...

Map of Bagger-Lambert papers--links, interviews http://sciencewatch.com/dr/erf/maps/08decerfBaggETRFM/#156486489 This is an interesting development in String/M, very recent, most papers just appeared in the past year or two. The map shows the most highly cited papers and their approx. degree...

This is a general question... What is the difference between showing that a map is well-defined and that it is injective? To prove both can't you show that, given a map x, and elements a,b if x(a)=x(b) we want to show a=b.

Is a projection a quotient map? I think a quotient map is an onto map p:X-->Y (where X and Y are topological spaces) such that U is open/closed in Y iff (p)-1(U) is open/closed in X. And a projection is a map f:X-->X/~ defined by f(x)=[x] where [x] is the equivalent class (for a...

Homework Statement Let G={(a,b)/ a,b\inZ} be a group with addition defined by (a,b)+(c,d)=(a+c,b+d). a) Show that the map\phi:G\rightarrowG defined by \phi((a,b))=(-b,a) is an automorphism of G. b) Determine the order of \phi. c) determine all (a,b)\inG with \phi((a,b))=(b,a)...

Hi all! Does anyone know a general method for determining the image of a lin map? I´m aware of the definition if im, but how could I determine it. Maybe it would be useful to show this on some examples :)

Homework Statement Two questions: 1) Show that deg(f(g(x)) = deg(f)*deg(g) 2) f: Sn -> Sn deg(f) is odd then show there exists a pair of antipodal points that are mapped to antipodal points The Attempt at a Solution 1) I have tried the method of just counting preimages, but i don't...

http://www.stumbleupon.com/toolbar/#url=http%2525253A//www.eigenfactor.org/map/maps.htm

Homework Statement Draw a contour map of the function showing several level curves. f(x,y) = x^3 - y Homework Equations f(x, y) = x^3 - y The Attempt at a Solution I think I should be finding the domain and range, but other than that I am not sure what else I need to do.

Homework Statement Prove that the nonempty fibers of a map form a partition of the domain. The Attempt at a Solution Ok so we have some map phi: S -->T And we want to show that its pre-image phi-1(t) = {s in S | phi(s)=t} forms a partition of the domain. Im really confused here. I assume...

Derive the circuit that implements the state table http://silvercurvemedia.com/alex/flyers/state%20table.jpg The Attempt at a Solution I know you can get your equations for the circuit from either the table itself or through a Karnaugh map, but I prefer using a karnaugh map. How exactly would...

I need a conformal mapping that would map an ellipse or a circle to a line. I need this for the http://physics.indiana.edu/~berger/p506_fall2008/p506ps6.pdf" . As far as I can understand, z^2 + 1/z^2 makes the geometry similar to that of a plane on the horizontal axis with a circle centered...

Hi, I am having some problems understanding the degree of a continuous map g:circle --> circle I have found a definition in Munkres (pg 367) that I can't really understand (I'm an engineering student with little algebraic topology) and one in Lawson (pg 181), Topology:A Geometric approach...

Homework Statement Consider f: R^{m+1} - {0} -> R^{(m+1)(m+2)/2}, (x^{0},...,x^{m}) -> (x^{i} x^{j}) i<j in lexicografical order a) prove that f is an immersion b) prove that f(a) = f(b) if and only if b=±a, so that f restricted to Sm factors through an injective map g from Pm. c) show g...

Please, help me! Suppose T is a linear map and dim(Im(T))=k. Prove that T has at most k+1 distinct eigenvalues. Thank you in advance!

Homework Statement Suppose that V and W are finite dimensional and that U is a subspace of V. Prove that there exists T \in L(V,W) such that null T = U if and only if dim U \geq dim V - dim W. Homework Equations thm: If T \in L(V,W), then range T is a subspace...

Very cool image. Does anyone know, is anything in the information we got from this so far at all surprising? Is it likely we will learn anything about gamma ray bursts from this or is more information

Homework Statement 50V | /\ | / \ | / \ |/ \ 0 |---1------2---3---- x(cm) | \ / | \ / | \/ -50V| best i could do, sorry don't know how to open picture up... its not to scale obviously but i...

Consider f: S1 -> S1: (cos 2 pi x, sin 2 pi x) -> (cos 2 k pi x, sin 2 k pi x). How to show directly from the homological definition (without using Hurewicz etc) that degree(f) = k?

http://space.newscientist.com/channel/astronomy/cosmology/dn14546-biggest-3d-galaxy-map-to-probe-dark-energys-history.html In this cosmic cacophony, one particular note was louder than the rest, and it survives to this day as a characteristic wavelength in the clustering of galaxies...

Recall that for an nxn matrix A, the (i,i)-minor of A is defined as M_{ij}(A)=detA(i|j), where A(j|i) stands for the matrix (n-1)x(n-1) obtained from A by removing the ith line and jth column. Also note that we can view det as a map from R^n x ... x R^n to R taking n vectors from R^n, staking...

Homework Statement This is actually a programming assignment, however it's very math involved. Given a set of points in R3 (x,y,z coordinates plus a weighted value) that are known to be coplanar, I need to draw an appropriately rotated, scaled, and colored plane intersecting the data. We...

Im reviewing material for the exam and came across this question: Let pi_1:RxR->R be the projection on the first coordinate. Let A be the subspace of RxR consisitng of all points (x,y) s.t either x>=0 or (inclusive or) y=0. let q:A->R be obtained by resticting pi_1. show that q is quotient...

I'm a bit confused as to how the text Tensor Analysis on Manifolds, by Bishop and Goldberg on page 6. The authors define the term power set as follows _________________________________________ If A is a set, we denote by PA the collection of all subsets of A, PA = {C| C is a subset of A}...

[SOLVED] The four color map?? so i guess most of you know about the four color map theorm. i read about it in a book a couple of days ago and had some idle brain time today while driving a tractor. i scribbled out some maps on the dirt on the windows and always seems to enclose one region...

Homework Statement Find the linear map f:R^2 \rightarrow R^3, with f(1,2) = (2,1,0) and f(2,1)=(0,1,2) Homework Equations The Attempt at a Solution I actually don't understand this task. PLease help! Thank you...

[SOLVED] Show map is injective Homework Statement Going crazy over this. Let 1<p<2 and q>=2 be its conjugate exponent. I want to show that the map T: L^p(E) --> (L^q(E))*: x-->T(x) where <T(x),y> = \int_Ex(t)y(t)dt is injective. This amount to showing that if \int_Ex(t)y(t)dt=0 for all...

The question is to prove for finite dimensional T: V to W, T is injective iff there exists an S: W to V such that ST is the identity map on V. I can't quite make the connection between injectivity and the identity map. any suggestions? thanks in advance.

[SOLVED] form of a linear map Homework Statement Say E is a linear space (not necessarily of finite dimension), and R is the real numbers. Say we have a (contiuous) linear form T from E x R to R. Can we say T is of such and such a form? Particularily, can we say that T=g1+g2 where g1:E-->R...

Can someone explain how to create a function that will map an interval of the real line onto some other interval? Is there a general method? Can you demonstrate? (30 140) to (200, 260)? Thanks, Diffy.

At Perimeter Institute, Bianca Dittrich recently gave a survey introduction to (non-string) QG with Lee Smolin and Leonard Susskind asking questions among other. The talk video is online PIRSA 07120030 and the title was Introduction to Quantum Gravity I think of this as a kind of QG map from...

hello, I've been reading some proofs and in keep finding this same argument tyo prove that a linear map is injective viz, we suppose that t(a,c) = 0 and then we deduce that a,c = 0,0. is it the case that the only way a linear map could be non injective is if it took two elements to zero? i.e. t...

I am a believer that globalization is not only unavoidable, but also that in the long term it is good for everyone. However, we see tremendous inequities between developed and developing nations in the labor and environmental protection laws, safety laws, enforcement of these laws, and oversight...

QG has several approaches developing rapidly and it's not easy to maintain perspective. I'll update a rough outline map made earlier. We can use it to help know what papers to expect during the next couple of months and what developments to be prepared for. A. Three main sectors of...

This is not directly a homework problem, so I opted not to place this question there. From what I have read/gathered from the internet/my textbook, a quotient mapping is any surjective, continuous mapping from a space X to a space comprised of the equivalence classes of all x in X from a...

Homework Statement Decide whether each map is an isomorphism (if it is an isomorphism then prove it and if it isn’t then state a condition that it fails to satisfy). Homework Equations f : M2×2 ---- P^3 given by: a b c d --- c + (d + c)x + (b + a)x^2 + ax^3 The Attempt at...

Is there a diffrence between a map and a transform or are they the same thing? My math book uses the term map but i studyed transforms in lin alg and they seem like the same thing. please help me get this straight in my head.