Dual Definition and 354 Threads

Homework Statement Let V be a finite dimensional vector field over F. Let T:V→V Let c be a scalar and suppose there is v in V such that T(v)=cv, then show there exists a non-zero linear functional f on V such that Tt(f)=cf. Tt denotes T transpose. Homework Equations Tt(f)=f°T...

Homework Statement Dual plate capacitor with two dielectric slabs placed between the capacitors and a battery supply's a voltage across the capacitors. The slabs are not equal in dielectric permeability. What is the charge at the interface of the two slabs? Homework Equations The...

Bit of background about me. It's a bit long, but I really need advice. I am a 24 year old living in an economically hard hit area of the country. I have dual degrees in psychology and english, and am currently working in a job that doesn't require my degrees. Originally, I went to school...

http://farm7.static.flickr.com/6125/6203213456_7daabe9662.jpg" This is my first post and I've never been here so I'm not sure this is where i should post my question, but if I'm wrong, pls correct me. This force sensor is to load my truck ontop of that shaft to determine it's drag force...

Hi, I want to know more about Dual Gate MOSFETs, i.e, their structure, working, advantages etc... Googling "Dual Gate MOSFET" didn't help at all! So please suggest some sources (online) where I can find more information on them. Also, where can I find more information on current...

Hi, Was wondering how dual input power strips work. I've seen them in data center racks, they have 2 mains power inputs wired to separate mains circuits. if one breaker trips then the strip still receives power from the other circuit. Do these strips have both power circuits wired to all the...

Homework Statement Light propagates as waves, but exchanges energy as particles Homework Equations I don't understand the second part, i.e., light exchanges energy as particle. I need the help of members in this regard The Attempt at a Solution

I've been reading Ballentine, Chapter 1. Have I got this the right way around? Taking our inner product to be linear in its second argument and conjugate linear in its first, the (continuous?) conjugate space of a Hilbert space \cal{H} is the following set of linear functionals, each identified...

My background in linear algebra is pretty basic: high school math and a first year course about matrix math. Now I'm reading a book about finite-dimensional vector spaces and there are a few concepts that are just absolutely bewildering to me: dual spaces, dual bases, reflexivity and...

hi, anyone can provide a simple explanation of what is a dual vector space? i have scoured the net and the explanations are all a tad too complicated for my understanding :( thanks

I have a question about mappings that go from a vector space to the dual space, the notation is quite strange. A linear functional is just a linear map f : V → F. The dual space of V is the vector space L(V,F) = (V)*, i.e. the space of linear functionals, i.e. maps from V to F. L(V,F)=...

Howdy, I need help sorting out a plan... again. It has come to my attention, the various opinions on how hard it is for a bachelors in physics to get a job. Here's what i originally had in mind: B.S. physics -> get a job -> M.S. & Ph.D. physics. It is indeed a crude plan but to specify the...

Hello, I am currently a Jr. in high school and I am very interested in physics and computers. I would like to get a Ph.D. in physics (with emphasis of quantum mechanics or particle physics). For a career I would eventually like to build/research dealing with quantum computing, or be a particle...

Hi, I'm trying to understand the natural transformation from V to V**, and the book has the theory but I think I'm needing an example. Lets say V=R^2 a vector space over K=R. B={(1,1),(1,-1)} a basis of V B={x/2 + y/2, x/2 - y/2} a basis of V* v = (3,2) a vector of V I want to get a...

Homework Statement straight wire along z axis carries charge density \lambda traveling in +z direction at speed v. construct field tenor and dual at point (x,0,0_ Homework Equations E=(2\lambda /4\pi\epsilono r)r^ B=(\muo I/2\pir)\phi^ The Attempt at a Solution I just don't get...

Homework Statement show that if V=M \oplus N, then V^*=M^o+N^o 2. The attempt at a solution So I need to prove for any f \in V*, f(\epsilon)=(g+h)(\epsilon), where g\in M^o and h\in N^o. (g+h)(\epsilon)=g(\epsilon)+h(\epsilon)=g(\alpha+\beta)+h(\alpha+\beta)=g(\beta)+h(\alpha), where\alpha...

Homework Statement Find the current in each branch of the circuit shown in the diagram (attached) if: V1 = 1V V2 = 4V R1 = 1\Omega R2 = 2\Omega R3 = 1\Omega Homework Equations V=I*R The Attempt at a Solution Okay, so I know that the voltage will be even across the parallel...

EDIT: finite dimensional only! Hello, I would like to ask a question; I understand that the cannonical "evaluation map" ( (p(v))(f) = f(v) , f is a functional, v in V ) from V -> V** is a "natural" isomorphism ( we don't have to select any bases, the isomorphism relies on no choices ), so V...

Hi: In the case of a finite-dimensional normed space V, it is relatively-straightforward to show that the kernel of any element of V* has 1 . ( Assume DimV=n): We take a linear map L:V-->F ; F the base field. We choose a basis to represent L, then we consider F as a vector...

Hi, Analysts: I was just looking for a nice proof that when V is an infinite-dimensional normed space, then V and V* are not isomorphic ( I think there is an exception if V is a Hilbert Space, by using Riesz Representation ). Also: while V is not always isomorphic to V* in the...

Homework Statement Let V = P_n(F), and let c_0, c_1,..., c_n be distinct scalars in F. For 0 <= i <= n, define f_i(p(x)) = p(c_i). Prove that {f_0, f_1,..., f_n} is a basis for V*. Hint: Apply any linear combination of this set that equals the zero transformation to p(x) =...

As E* is defined in some book as Hom(E, MXR). What could be the isomorphism between dual vector bundle E* and Hom(E, MXR)?

I am building an axial flux generator with dual rotor and single stator. I was doing calculations and have a magnet pole pair question i need help with, there are 12 magnets on each rotor with North pole on one rotor across from South pole on the other rotor. Since there are 24 total magnets...

Homework Statement An emergency supply consists of a small diesel engine driving an alternator. The output of the alternator is rectified and smoothed to produce DC. This has has to supply 10 amps of 110V emergency lighting and charge a 110V battery of internal resistance 2 ohms, If the...

Hello, I'm investigating duality for plane curves, and I came across an 'original' interpretation of the Biduality theorem , that uses the notion of caustic curve. Because everything is still very obscure to me, I try to share the whole with you, in the hope that we can help to fix ideas...

Let V be the space of polynomials of degree 3 or less over \Re. For every \lambda\in\Re the evaluation at \lambda is the map ev_{\lambda} such that V \rightarrow \Re is linear. How do we find the coefficients of ev_{2} in the basis dual to \{1,x,x^2,x^3\}?

Hey guys! I am going crazy... most books don't cover this and instead assume that the manifold is Riemannian or pseudo-Riemannian and has a metric tensor defined on it. I want a "generalized" hodge star. I have an orientable smooth manifold, that's IT. I have heard that there is a way to...

i need a link which can help me better understand primal and dual problems along with simplex Any help would be appreciated Thanks

Let us say we have source that can emit a single photon. We can in principle detect when the photon leaves the source due to the momentum kick. Now let us say this single photon passes through both slits and forms a dot on the far right of the screen. Now if we draw paths through the two slits...

I recently had a conversation with a friend (who for some reason likes number theory) about these split-complex numbers and dual numbers. I'm more into topology, so I've never heard of them and he brought up that the modulus (I've only heard this term used for complex numbers) of the...

why do we use a dual power supply? Why, for instance, do we use +12 and -12 volt instead of just a 12 volt power supply.

I was reading about dual spaces and dual bases in the book Linear Algebra by Friedberg, Spence and Insel (FSI) and they give an example of a linear functional, f_i (x) = a_i where [x]_β = [a_1 a_2 ... a_n] denotes the matrix representation of x in terms of the basis β = {x_1, x_2, ..., x_n} of...

Hello, I had read about the dual nature of electrons and the quantum numbers for some time ago and was always confused. 1-What does dual nature of electron mean? Does it mean that the electron moves in a sort of wave like motion around the nucleus? Where do the sub-shells and orbitals fit in...

I am familiar with the dual slit experiment up to the point where measuring at one slit made the interference pattern collapse. My question is has anyone tried using a sensor of some kind that has no memory or output? Does the observer have to be sentient? I have a feeling someone has...

Finite Dimensional Inner-Product Space Equals its Dual!? Let V be a finite dimensional inner-product space. Then V is 'essentially' equal to its dual space V'. By the Reisz Representation theorem, V is isomorphic to V'. However, I've been told that V=V', which I am having a hard time...

We just had two dual flow toilets installed in our house. They have two modes of flush, a small flow flush for #1 and a somewhat larger flow for #2. The small flow is really good, it uses very little water compared to our old style toilets. However the large flow is insufficient to clean the...

Hey guys, i am looking for some primer on conformal, dual conformal symmetry, respectively. I have to read a lot of stuff about scattering amplitudes for uni and in recent papers people talk a lot about these symmetries... unfortunately i am not so familiar with them, so does any of you know...

So I'm pretty sure I understand the formalism of dual vector spaces. (E.g. there exist objects that operate on vectors and take them to scalars. these objects themselves form a linear vector space). But I'm having difficulty understanding where this comes from intuitively. How would I know...

This is a very silly question. I can't believe I have forgotten. I have a 30v bench power supply and I am looking to test an op-amp running at +/- 15v. I have a supply which has a negative output/ positive output and inbetween a green common/earth output. How do I wire them to produce the +/-...

My laptop has a duel core Intel Centrino processor. Whenever I write programs in C/C++ in Visual Studio and run programs which should execute at full speed only one core seems to be doing anything. Some programs seem to be able to make full use of both cores, is this possible in Visual Studio?

Ok I'm trying to calculate the Dual Faraday Tensor, but I'm having trouble with the notation I think... *F^{ab} = \frac{1}{2}E^{abcd}F_{cd} where E is the levi-civita symbol. I'm correct in that E^(1234) = 1 for (1234,3412,2341,4123) -1 for (4321,3214,2143,1432) 0 otherwise...

What are the units of vectors and dual vectors? And where do the the units in the metric need to be placed so that V^{\mu}V_{\mu} is a scalar? Taking charge density and current density that combine as a 4-vector, J^{\mu} \partial_{\mu}, and it's dual vector J_{\mu} dx^{\mu}, which units go...

Background. We define vectors in general relativity as the differential operators \frac{\cdot}{d\lambda}=\frac{dx^\mu}{d\lambda}\frac{\cdot}{\partial x^\mu} which act on infinitessimals--dual vectors, df=\frac{\partial f}{\partial x^\mu} dx^\mu \ , as linear maps to reals. However, both...

So I asked this question about Rigged Hilbert Space https://www.physicsforums.com/showthread.php?t=435123 And one of the problem I have understand Rigged Hilbert Space is that it involves taking the dual of a particular dense subspace of Hilbert Space and I of course have no clue what the...

Hi guys, I'm looking at potentially dropping my computer engineering degree from my dual degree plan (EE is my other degree). I would still maintain an emphasis in computer engineering for my degree, but do you think by doing this I will be harming my chances to be employable after...

Homework Statement Let ||\cdot || denote any norm on \mathbb{C}^m. The corresponding dual norm ||\cdot ||' is defined by the formula ||x||^=sup_{||y||=1}|y^*x|. Prove that ||\cdot ||' is a norm. Homework Equations I think the Hölder inequality is relevant: |x^*y|\leq ||x||_p ||y||_q...

Homework Statement Prove that if m < n and if y_1,...,y_m are linear functionals on an n-dimensional vector space V, then there exists a non-zero vector x in V such that [x,y_j] = 0 for j = 1,..., m Homework Equations The Attempt at a Solution My thinking is somehow that we...

thanks everyone I found an answer

Homework Statement For the Banach space X = C[0,1] with the supremum norm, fix an element g \in X and define a map \varphi_g : X \to \mathbb{C} by \begin{align*} \varphi_g(h) := \int^1_0 g(t) h(t) dt, \qquad h \in X \end{align*} Define W := \{ \varphi_g | g \in X \}. Prove...

I'm a beginner at differential geometry. I have a problem about dual space. I understand why we use \left\{\frac{\partial}{\partial x^{\mu}}\right\} as the bases in vector space, but I have no idea why we use \left\{ dx^{\mu} \right\} as the bases of dual space. What is the reason of...