Dual Definition and 354 Threads

[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...

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:

I have an acer aspire30002 and i connected a dell flat panel monitor to it. The thing is I can never get them to display separate screens. I got them to display the same thing earlier but now only one at a time. Does this mean that the video card does not support dual monitors?

While I've worked with an awful lot of motors, including making simple ones and repairing several others, I don't know the technical aspect of what governs the no-load speed of a DC unit. Specifically, I have 3 really nice 12VDC 1/2hp wheelchair drive motors with gear trains. They're extremely...

Ok, so we learned about rail guns today (they are so freakin' cool), and I understand how it moves one rod down the rails... however, what happens if there are two? Won't both move down the rails (away from battery) since the current is flowing clockwise, or will they repel each other?

I want to get into the R&D team at one of the big 3. I am currently a dual major in electrical engineering and mechanical engineering, which is a 167 credit hour program. I am currently a second semester junior in EE and a second semester sophomore in ME. I am going the EE/ME dual major route...

In my lecture note about tensor it states: As element of integration over the hypersurface it is more convenient to use the 4-vector dS^i , dual to the tensor dS^ikl: dS^i = -1/6 e^iklmdS_klm ,dS_klm = e_iklmdS^i What is the meaning of dual? How the -1/6 comes from? yukyuk

I am reading ahead for my Group Theory introduction to QFT and I have a question about the dual representation. If the dual representation is the same as the ordinary representation, that is to say the ordinary representation is "real", how do we represent anti-particles in this case? This...

Does anyone know if anything in your average room (besides a kitchen) emits enough heat to decently warm up a piece of food? I had a feeling a CRT monitor would do but i only have an LCD now and i want to heat up this cherry turnover! Oh, and I only use CF bulbs in my room...

If you have a five gallon jug of water with a 1/2 inch spout, and it is laid on its side, because there is no other opening in the jug it empties as air spills into the spout and replaces the water, but if the jug would have another 1/2 inch spout on it, now on top of the laid down jug, Would...

I've worked it out and due to offering limitations it will take me 3 more years to do the former, and 2 more years to do the latter. I've already been in university for 2 years. The courses I'd need in order to accomplish both are listed below: For the dual major in physics/math with...

dual major in chemistry and physics or physics and math oops, I meant dual major in chem and physics OR physics and math. So what do you think is better for someone who wants to go into theoretical physics? Should I go for a dual major in chem and physics and a minor in math, or a dual...

Fall semester: Intermediate Inorganic Analytical Chem Analytical chem lab Physical chem 1 physical chem 1 lab Advanced Eng. Math Contemporary Physics Contemp. lab :cry: Spring Semester: Quantum Mechanics Physical chem 2 Physical Chem 2 lab Linear Alg. Advanced Organic...

Hi, could someone show me how to express \frac{\partial G^{\mu\nu}}{\partial x^\nu} = 0 which are Maxwell's equations, G is the dual tensor, in terms of the field tensor F: \frac{\partial F_{\mu\nu}}{\partial x^\lambda} + \frac{\partial F_{\nu\lambda}}{\partial x^\mu} + \frac{\partial...

Hi, I have a question about calculating the error of the transducer. A pressure transducer exhibits a temperature sensitivity of 0.05 units per degree Celsius and a pressure sensitivity of 5 units per MPa. If the temperature changes 30 degrees celsius during a measurement of a pressure of...

Fisrst excuse me if the topic has already been addressed. I have made a quick research and i didn´t fint it. I talk about these: http://news.bbc.co.uk/1/hi/sci/tech/4357613.stm A preliminar interpretation of it was as a black hole. Someone suggested me to do a researtcho for...

I realized some time ago, that there was no singular term that refers to both genders! This is really quite annoying, since I've been using "him/her" quite a bit, and it gets tedious. Am I mistaken, and there actually is one, or can we all just agree on one? :D:D:D:D:D I propose "xem"...

Here's one from my HW: Two blocks are connected by a massless string on a triangle with a pulley at the top corner. The angle of the left corner is 35 degrees. the angle on the right is 60 degrees. the left block equals 7kg and the right is 9 kg. mu k = 0.25 Determine acceleration of...

How much can it boost PC performance? Worth it or not?

My friend has a problem. He has a computer that has one working internet and his other computer's internet is down. They are in separate rooms but are connected by an extension cord. They are both connected to the same modem, any ideas why one is working and the other isnt? (They share the same...

I don't know why Britain wants democracy everywhere especially in commonwealth countries, since they have got a queen of their own. Is that democracy? The invaded Iraq to free it from a dictator who had his own parliment. The queen has got a parliment shouldn't she be thrown off. It says in a...