Map Definition and 403 Threads

Not sure if this is the right category but i need help. On a map of a school, 3 inches represents 9 feet. How many inches would represent 1 foot 6 inches?

Homework Statement Let R be an arbitrary ring, B and B' be left R-modules, and i: B' \to B be an R-module morphism. Show that if the induced map i^*: \operatorname{Hom}_R(B,M) \to \operatorname{Hom}(B',M) is surjective for every R-module M, then i: B' \to B is injective. The...

Here is the question: Here is a link to the question: Linear Algebra Problem *Help Please*? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Consider the field Q(\sqrt{2}), viewed as a vector space of dimension 2 over Q. Let r + s\sqrt{2} \in Q(\sqrt{2}), and define the multiplication map M_{r+s\sqrt{2}}: Q(\sqrt{2}) → Q(\sqrt{2}) by M_{r+s\sqrt{2}}(\alpha)= (r+s\sqrt{2})*\alpha In other words...

I am working on a Bachelors thesis and need to make a grid on a map over a entire floor. Can someone show me how to do this in matlab?

I've two routes in google map: i) A ---> B ii) C ---> D How can I determine if these routes overlap or not?

My textbook says that "a chart or coordinate system consists of a subset U of a set M, along with a one-to-one map \phi :U\rightarrow\mathbf{R}^n, such that the image \phi(U) is open in \mathbf{R}^n." What's the motivation for demanding that the image of U under \phi be open?

Hi, I'm trying to figure out a few questions on a practice exam that I'm working on for my Intro to Logic Systems class and could use some help. One of the questions (and the others are similar) says: Determine the minimized realization in the sum-of-produicts form using literals of the...

Hi! I was wondering why it is possible to write any proper orthochronous Lorentz transformation as an exponential of an element of its Lie-Algebra, i.e., \Lambda = \exp(X), where \Lambda \in SO^{+}(1,3) and X is an element of the Lie Algebra. I know that in case for compact...

Can you help me to construct a 1-1 mapping from real numbers onto non-integers? thanks

I have what I hope to be just a simple notation/definition question I can't seem to find an answer to. I'm not going to post my homework question, just a piece of it so I can figure out what the question is actually asking. I have a function i:A --> X I also have a continuous function g: A...

I quote an unsolved question from MHF posted by user jackGee on February 3rd, 2013. P.S. Of course, I meant in the title and instead of an.

I quote an unsolved problem from MHF (Linear map problem) posted by user jdm900712

Homework Statement Let V be a vector space over the field F. and T \in L(V, V) be a linear map. Show that the following are equivalent: a) I am T \cap Ker T = {0} b) If T^{2}(v) = 0 -> T(v) = 0, v\in V Homework Equations The Attempt at a Solution Using p -> (q -> r) <->...

So I have to implement a 4 input 1 output circuit. I am given the Karnaugh map (obviously a 4by4) and have to build the circuit. I have already determined the essential prime implicants for my map and three possible permutations of nonessential prime implicants. So let's say I pick a...

Whether a continuous and locally one-to-one map must be a (globally) one-to-one map? If the answer is not. Might you please give a counter-example? Thank in advance.

I've been poking around, learning a little about homology theory. I had a question about the boundary operator. Namely, how it's defined. There's two definitions I've seen floating around. The first is at: http://en.wikipedia.org/wiki/Simplicial_homology The second, at...

Commutative ring, map R / ( I /\ J) -> ( R/I ) x ( R/J ) I quote an unsolved question posted in MHF (November 25th, 2012) by user needhelp2. P.S. Communicative note: Of course I meant in the title, commutative instead of communitative.

We are just looking for an example of a quotient map that is not open nor closed. Let π: ℝxℝ -> ℝ be a projection onto the first coordinate. Let A be the subspace of ℝxℝ consisting of all points (x,y) such that x≥0 or y=0 or both. Let q:A -> ℝ be a restriction of π. ( Note: assume that q was...

This is not actual "homework." I am building a POV globe and I want to get as accurate of a projection as possible. The images I will upload into the globe will be a simple 2 dimensional image projected onto a 3 dimensional plane. I have researched and it appears that a Mercator type map is the...

Homework Statement The Attempt at a Solution set x(t)=1+∫2cos(s(f^2(s)))ds(from 0 to t) then check x(0)=1+∫2cos(s(f^2(s)))ds(from 0 to 0)=1 then the initial condition hold, by FTC, we have dx(t)/dt=2cos(tx^(t)), then solutions can be found as fixed points of the map but for...

Homework Statement Find the eigenvectors and eigenvalues of the differentiation map C1(R) -> C1(R) from the vector space of differentiable functions to itself. Homework Equations The Attempt at a Solution Hi, I'm not entirely sure how to go about this, because would the...

Homework Statement Suppose H is an infinite cyclic subgroup of Z. Show that H and Z are isomorphic. Homework Equations We know that any infinite cyclic group H isomorphic to Z. H = <a> ≠ <0> |a| = ∞ The Attempt at a Solution Define f : Z → H | f(k) = ak for all k in Z. We...

Suppose T belongs to L(V,V) where L(A,W) denotes the set of linear mappings from Vector spaces A to W, is such that every subspace of V with dimension dim V - 1 is invariant under T. Prove that T is a scalar multiple of the identity operator. My attempt : Let U be one of the sub spaces of V...

How bad is my statistics knowledge based on the following mind map? Any concepts which aren't bold are the concepts that I know; the bold ones are the ones I'm currently learning. The mind map in question: http://i.imgur.com/4He3f.png What should I learn next based on my current...

Homework Statement As in title. Homework Equations Described in my attempt. The Attempt at a Solution Where do I go from here? I need to show that those 2 unioned sets are open in A. I'm not seeing it

Homework Statement let a be the vector [2,3,1] in R3 and let T:R3-->R3 be the map given by T(x) =(ax)a State with reasons, the rank and nullity of THomework Equations The Attempt at a Solution Im having trouble understanding this... I know how to do this with a matrix ie row reduce and no. of...

Homework Statement Show that B = {x2 −1,2x2 +x−3,3x2 +x} is a basis for P2(R). Show that the differentiation map D : P2(R) → P2(R) is a linear transformation. Finally, find the following matrix representations of D: DSt←St, DSt←B and DB←B. Homework Equations The Attempt at a...

Hi there, I'm reading a report about the efficiency of the drive train of an electric car. The author recorded the speed and acceleration of the car over a period of time and created the graph below to illustrate the efficiency. Could anybody tell me what the relationship is between the...

Homework Statement Let D be a division ring, C its center and let S be a division subring of D which is stabilized by every map x -> dxd-1, d≠0 in D. Show that either S = D or S is a subset of C. 2. The attempt at a solution I haven't actually started working on it yet because I am not...

Hi all, I need help with a paragraph of my book that I don't understand. It says: "the map sending all of ℝ^n into a single point of ℝ^m is an example showing that a continuous map need not send open sets into open sets". My confusion arising because I can't figure out how this map can be...

The definition of a homomorphism is that it must preserve some algebraic structure, so if I transform a vector space using homomorphism between vector spaces (linear map), the result must be a vector space too, correct? Now, if "v" and "w" are two vectors in a vector space V, than "(v + w)"...

Hi all. I am new here and I am having difficulty figuring out what exactly is required of me in this question. If someone could be so kind as to explain. For this part of the project we will consider the evolution of a discrete dynamical system given by a logistic map. We will consider a...

Hi! Suppose we have a topological space X, a point x\in X and a homomorphism \rho:\pi(X,x) \rightarrow S_n with transitive image. Consider the subgroup H of \pi(X,x) consisting of those homotopy classes [\gamma] such that \rho([\gamma]) fixes the index 1\in \{1,\ldots,n\}. I know that H...

Homework Statement If the set \Z of integers is equipped with the relative topology inherited from ℝ, and κ:\Z→\Z_n (where κ is a canonical map and \Z_n is the residue class modulo n) what topology/topologies on \Z_n will render κ globally continuous? Homework Equations The Attempt...

Hello All, I am a Masters student in Microelectronics and stuck at something very trivial. In implementing Pass transistors using K Map, i am facing some probs. For eg. consider the function bc(bar) now if you draw a k map the left downward 4 blocks will be filled with 1s. I don't understand...

Homework Statement I'm trying to show that a distance preserving map is 1:1 and onto. The 1:1 part was easy, but I'm stuck on proving it's onto... Homework Equations X is compact T(X)\subseteqX THere's a hint saying to consider a point y in X\T(X) and consider the minimum distance...

I need help calculating the exponential map of a general vector. Definition of the exponential map For a Lie group G with Lie algebra \mathfrak{g}, and a vector X \in \mathfrak{g} \equiv T_eG, let \hat{X} be the corresponding left-invariant vector field. Then let \gamma_X(t) be the maximal...

Homework Statement Does anyone know the process for finding the differential of of f:S→S' where S,S' are surfaces. My textbook explains how to do this when f is a vector valued function but in the problem that I am working on I have something like f(x,y)=(g(x),h(x),j(y)) rather than something...

Homework Statement Prove that the identity map \mathrm{id}_{S^{2k+1}} and the antipodal map -\mathrm{id}_{S^{2k+1}} are smoothly homotopic. Homework Equations N/A The Attempt at a Solution My attempt: Fix k \in \mathbb{Z}_{\geq 0} and let \{e_i\}_{i=1}^{2k+2} be the standard basis for...

consider we have a map. what condition should have our map that it has inverse?

Top down visual of near live wind trails in the US. Really neat! http://hint.fm/wind/ Now we just need it overlayed on google maps!

1. Let G be any group and x∈G. Let σ be the map σ:y→xyx⁻¹. Prove that this map is bijective. It seems to be written strangely, since it never really says anywhere that y is in G, but I guess that must be an assumption.2. bijective=injective+surjective. in order to prove injective, we need to...

Homework Statement The Attempt at a Solution For part ii) I wrote it out as a matrix, getting \begin{array}{ccccccc} 0 & 0 & 0 & 0 & ... & 0 \\ 0 & 0 & 2 & 0 & ... & 0 \\ 0 & 0 & 0 & 6 & ... & 0 \\ . & . & . & . & . & . \\ 0 & 0 & 0 & 0 & ... & N(N-2) \end{array} So...

I found some Matlab code that works. However, I am not sure how to alter it for my needs. How can I make the code work for this:##N_{t+1} = \frac{(1+r)N_t}{1+rN_t}##What needs to be changed? %%% MAKES A COBWEB PLOT FOR A LOGISTIC MAP % compute trajectory a=3.0; % parameter x0=0.2...

Suppose you've got a linear map U between two Hilbert spaces H1 and H2. If U preserves the inner product - that is, (Ux,Uy)_2 = (x,y)_1 for all x and y in H1 - is it necessarily unitary? Or are there inner product-preserving linear mappings that aren't one-to-one or onto?

I'm looking at Munkres: Topology Problems 1.2.4(c), 1.2.4(e), and 1.2.5(a). Problem 1.2.4(c) asks, "If g\circ f is injective, what can you say about the injectivity of f and g?" Problem 1.2.4(e) asks, "If g\circ f is surjective, what can you say about the surjectivity of f and g?" I concluded...

Hey guys, I've often seen in the definition of a Fiber bundle a projection map \pi: E\rightarrow B where E is the fiber bundle and B is the base manifold. This projection is used to project each individual fiber to its base point on the base manifold. I then see a lot of references to...

Google France Sued by Bottin Cartographes for Providing Free Map Services... So this is an interesting story... Unfortunately all the articles I have seen seem to be based on the same AFP article and the AFP article is rather lacking in information. Add to that my lack of french and I am...

I'm interested in the proper way to give a mathematical definition of a certain geometric property exhibited by certain maps from points to sets. Consider mappings from a n-dimensional space of real numbers P into subsets of an m-dimensional space S of real numbers. For a practical...