Dual Definition and 373 Threads

Hi guys I am interested in studying chemical engineering at university next year and also want to do a double degree with a bachelor of science. However I am having a hard time deciding what major would be the most useful...any advice would be greatly appreciated. Possible Majors (that...

It's been so long since I thought about this, I just need to know if this is correct. If I have the matrix representation of a linear transformation between vector spaces V and W, and I take the transpose of the matrix, am I in essence constructing the matrix representation of a...

Does anyone know if it is worth doing both Electrical Engineering and Mechanical Engineering? Does it help or hurt? Anyone know of a person who has done this and what was there outcome.

Hi everybody, I'm new (found this site while unwinding from a long week of paper-editing). Just for a quick reference, I'm currently pursuing a BS in biophysics and minors in math and chemistry... this place seems to be a good home for me... So I'm starting to think about life after...

I wonder if the mass term in the kinetic energy can be alterantively interpreted as a metric? And can energy be a form of inner product? I've found a few references that suggest these things, but I'm not sure how accepted they are. And I'm wondering if anyone can provide any better insight...

Hi, I am trying to sort out a few things about the dual and double dual of a normed space which has got me a little confused. Given a normed space X over \mathbb{R}, if Y is a subspace of X, what is the relationship between Y^* and X^*? Can Y^* be identified with some subspace of X^*...

Hi, actually someone already posted the same questions but I thought it would be weird to continue from that post as I have a lot of questions of my own. The assignment requires me to draw a schematic diagram of a dual output dc power supply, identify the sub sections that make up the power...

What is the importance of dual electromagnetic field tensor? Generally this is not included in the action. What will be the advantage/disadvantage if I include terms like F_{\mu \nu}\tilde{F}^{\mu \nu}, \tilde{F}_{\mu \nu}\tilde{F}^{\mu \nu} in the action? (The tilde denotes the dual tensor.)...

I'm designing a set of voltage and current sensors for use with a solar system. I have developed all of the circuits, but it requires both positive and negative voltage supplies. I want to use the classic design using a center tapped transformer with two regulators. But I'm not sure what will...

I'm having trouble with the power supply portion of an opamp circuit I'm working on. The supply is +/- 5 Volt using 7805/7905's. Half wave rectifiers provide the unregulated input with 1000uF input caps and 100uF output caps. AC is supplied by a 13VAC 'wall wart' with no center ground tap...

But the cannonical injection to not be an isomorphism?

I plan to take mechanical engineering and my university also offers the option of completing a concurrent degree in any area I wish. However, this process will take 5 years as opposed to 4 meaning I'll have to pay tuition/rent/expenses for an extra year. Would getting a mechanical + medical...

http://camoo.freeshell.org/25.8.pdf" Laura Latex source below. I won't be changing this if I edit the file, it's just for convenience if you want to grab latex code. n sec. 25.8, he says "recall the dual $^\ast F$ of the Maxwell tensor F. We could imagine a 'dual' U(1) gauge...

please see http://camoo.freeshell.org/dual_gauge.pdf" Thanks Laura

the primal problem was: min (x^T)Px i found g(r) and the partial derivative of g(r) w.r.t. x to be: x=-1/2(P^-1)(A^T)r i have found the dual problem to be: max -1/4(r^T)A(P^(-1))(A^T)r - (b^T)r subject to r>= 0 I am told to find x* and r* (which i think is just x and r): i have not...

In calculus on manifolds, within one of the problems of this book the dual space is indirectly defined. I'll quote: Let (R^n)^* denote the dual space of the vector space R^n. If x \in R^n, define \phi_x \in (R^n)^* by \phi_x(y) = \langle x, y\rangle. Now my problem is I just don't get...

Homework Statement Find the dual vector of the following tensor: 6 3 1 4 0 5 1 3 2 Homework Equations dj= EijkTik Where Eijk = 1 if ijk=123, 231, 312 Eijk = 0 if i=j i=k or j=k Eijk = -1 if ijk = 132, 213, 321 The Attempt at a Solution Ok...

[SOLVED] Linear Algebra Dual Basis Let V= R3 and define f1, f2, f3 in V* as follows: f1 = x -2y f2 = x + y +z f3 = y -3z part (a): prove that {f1, f2, f3} is a basis for V* I did this by using the gauss jordan method and showing that {f1, f2, f3} is linearly independent. Now...

[SOLVED] Linear Algebra - Dual Spaces Homework Statement (V and W are vector spaces. F is a field) "The space L(V,W) of linear maps from V to W is always a vector space. Take W = F. We then get the space V* := L(V,F) of F-linear maps V --> F. This is called the dual space of V." 1. Let V =...

[SOLVED] The continuous dual is Banach Homework Statement I'm trying to show that the continuous dual X' of a normed space X over K = R or C is complete. The Attempt at a Solution I have shown that if f_n is cauchy in X', then there is a functional f towards which f_n converge pointwise...

ice as in internal combustion engine, sorry for confusion Homework Statement I'm given an engine operating on the dual cycle and asked to find the thermal efficiency and the mean effective pressure. the compression ratio is 18:1, the temperature at the start of the compression 300K and the...

Propositional Logic - "There Exists" dual Homework Statement "State and prove the \exists-dual of 6.1.8" Section 6.1.8 shows how to change \vdash (\forall x)(\forall y)A \equiv (\forall y)(\forall x)A via this method: (Line 1) (\forall x)(\forall y)A (Hypothesis) (Line 2) (\forall...

My professor uses the notation Hom(V,\mathbb{R}) for the dual space of V. I usually see V* rather. What does the notation Hom(V,\mathbb{R}) stands for exactly? I suppose the domain of Hom is wider than just (vector spaces) x (their field). The notation suggest it is the set of homomorphisms btw...

I wasn't quite sure where to post this, as it isn't really a homework question. My professor is teaching us General Relativity from a post-grad book, and I don't have a lot of linear algebra under my belt. He lent me the textbook he's teaching from the other day, and I got stuck when I got to...

I'm already majoring in physics but plan on majoring in math as well. If I'm aiming to go into astronomy or astrophysics, I assume the math BS would help like steroids, right? And how important should it be for me to get into the state university to study said fields if I plan on going to...

Not my homework It's in the textbook - lectures of diff geo by s.s.chern Just put them down in a clearer way Could anybody explain the questions in the pic ? http://x7d.xanga.com/be6d931344030137094065/z100635368.jpg"

I am trying to prove the following result (I am using the notation of Felsager, Geometry, Particles and Fields) The Hodge dual of a k form "F" in n dimensions (here I work in Euclidean space) gives an n-k form with covariant components (\,^* F)_{a_1...a_{n-k}} = \frac{1}{k!} \sqrt{g}...

Hi, I'm in dire need for help in my assignment. I have been asked , a), to research on a dual output DC power supply (Output = +15v and -15v) of not more than 15 components and to identify the different sub-sections that make up the power supply on the schematics. And, b), give an explanation...

HIGH o/p dual power amplifier (! HELP !) i have attached the cct diagram i found about this IC BA5417 it is a power amplifier as one can see pins 11 & 12 are input but how exactly does on give this input i plan to give input from my discman so there will be one ground wire and the two...

Hello all. I wasd beginning to feel at home with vectors and covectors but while trying to fully understand the concepts this query came up._________ Excuse the lack of rigorous definition but I think you will realize what I am aiming at. Take a geometrical vector in a finite...

So I've set up my computer to dual boot into WinXP or Fedora Core 6. As recommended by some walkthroughs I found, I've created a FAT32 partition for passing data back and forth between WinXP and linux. Alas, it only has 8 character filename support. I would like to have a partition for...

Homework Statement An extract from my notes reads that "every boolean law has a dual: any valid statement is also valid with:" . replaced with + + replaced with . 0 replaced with 1 and vice versa. Homework Equations None The Attempt at a Solution I have no clue what this...

Whilst trying to refresh myself on what a dual space of a vector space is I have confused myself slightly regarding conventions. (I am only bothered about finite dimensional vector spaces.) I know what a vector space, a dual space and a basis of a vector space are but dual bases: I seem...

Hello all, I was wondering if anyone could help me figure out some differences between all the different types of processors out there for computers. I am a graduate student learning about CFD, and my advisor wanted me to check out some different processors because we would like to get new...

I'm leaning more and more towards this option, but I'm wondering if it'll ultimately be worth it. In your experience, will the MBA ultimately lead to a higher salary and/or more leadership than a MS alone?

The school I'm considering has a program called BPPME, that offers a Bachelors in Physics and a Masters in Mechanical Engineering in as little as 5 years (I'll probably do 6 years because it's cheap and I usually need a little more time to fully grasp some concepts)...does this sound worth it...

Ludicrous? Would this look good on a resume when I go to apply to grad schools for solid state physics? I will have a 3.5 GPA (hopefully), REU experience and hopefully decent GRE scores. I'll be a member of eta kappa nu (EE honors society), and sigma pi sigma (physics honors society) and...

let A \hookrightarrow B be a continuous inclusion map from A to B. A, B are two topological spaces. A \subset B what can we say about the induced map between topological dual spaces B^* \hookrightarrow A^* ? is it continuous and injective?

I am trying to prove that T'' = T (where T'' is the double transpose of T) by showing that the the dual of the dual of a linear finite vector space is isomorphic to the original vector space. i.e., T: X --> U (A linear mapping) The transpose of T is defined as the following: T'...

So what's the difference between these two technologies? seems to me they're almost the same, no?

It seems I can finish my dual degree in EE/physics in 3 more semesters and be out after a total of 4.5 years with a dual degree in EE and physics with a minor in chemistry. However, these last three semesters will be a rather heavy course load of 18 credits per semester. The other option is to...

Hi, a quick and easy one I hope someone can help me with. What would be the general expression for a DSB-AM modulated signal in terms of the Carrier Signal C(t), Baseband Signal S(t) and the modulation index m? Many Thanks

Hello all, I'm running a stochastic simulator for chemical rate equations and I'd like to know how to specifically impelement a dual core solution on my AMD athlon 64 X2 4200+ processors. When I run the task manager with the simulator running, it is apparent that both cpus are running...

I am thinking of doing something called a "3+2" program, where I spend 3 years at my liberal arts college and 2 years at the Columbia Fu School of Engineering. I come out with a B.A. in any type of science or math from the liberal arts college and a B.S. in applied math (or any type of...

Can someone prove this to me? I know that if you have a finite dimensional vector space V with a dual space V*, then every ordered basis for V* is the dual basis for some basis for V (this follows from a theorem). But if you're just given an arbitrary vector space V. Let's say the Space of R^n...

I have a computer dual booted with Fedora Core 5 and Windows XP. I only have Fedora on so I can learn how to use Linux and XP is my primary OS. Whenever I boot up it gives me a few seconds to choose between XP and Fedora otherwise it loads Fedora by default. How do I change this to have...

I have noticed that the only processors that Intel makes that are both dual core and offer hyper threading are their Extreme Edition series. These processors are priced above nine hundred dollars! When do you guys think that they will sell a processor that offers both these features at a price...

I've been starting to study some things about representation theory. I've come to the point where they introduced the dual of a representation. Suppose that \rho is a representation on a vector space V. They then define the dual representation \rho^* as: \rho^*(g) = \rho(g^{-1})^t: V^*...

Specifically LGC is dual to RS theory with an extra (large) time-like dimension, as reported by Parampreet Singh today in: http://arxiv.org/PS_cache/gr-qc/pdf/0603/0603043.pdf This is the first connection between loop quantum gravity and string theory that I am aware of. The need for an...

If it is not urgent to upgrade your PC, you should wait for the 65nm and Dual Core 64-bit processor based PC/Notebook, it is a great improvement to cope with Windows Vista.:bugeye: