Dimension Definition and 929 Threads

I can't make this question work, so I'm hoping that someone here will be able to help guide me towards a solution. I began with F=ma, and wrote down the equations of motion for each of the masses. a) 2mx..1 = -kx1 -k(x1 -x2) and b) mx..2 = -kx2 +k(x1 -x2)Then I added b to a, and subtracted...

I've attached a copy of the problem and my attempt at a solution. This seems like a relatively straightforward question to me, but my answer seems to be the exact opposite of what the answer key says. I reach the conclusion that the answer is C, but the answer is apparently D. I'm...

Find the dimension of the subspace of M2;2 consisting of all 2 by 2 matrices whose diagonal entries are zero. ? i know that the dimension is the number of vectors that are the basis for this subspace ,but i cannot figure out what is the basis for this subspace ? any help will be...

My doubt is that is dimension of a 2nd order homogeneous equation of form y''+p(x)y'+q(x)=0 always 2 ? or dimension is 2 only when p(x),q(x) are contionuos on a given interval I..??

This is dealing with computer vision, but the only part I'm having trouble understanding is a step in the matrix math. So it seems appropriate it should go here. The paper/chapter I'm reading takes one of those steps saying "from this we can easily derive this" and I'm not quite sure what...

I've been struggling with this problem for about two weeks. My supervisor is also stumped - though the problem is easy to state, I don't know the proper approach to tackle it. I'd appreciate any hints or advice. Let V be an random k-dimensional vector subspace of ℝn, chosen uniformly over...

Use the dimension theorem to show that every polynomial p(x) in Pn can be written in the form p(x)=q(x+1)-q(x) for some polynomial q(x) in Pn+1. I need to see all the steps so that I understand how to do it. PLease and Thank you

Homework Statement The electric field between two circular plates of a capacitor is changing at a rate of 1.5x10^6 V/m/s (ΦE). If displacement current at this instant is Id=0.80x10^-8A, find the dimensions of the plates. Homework Equations Id=ΔQ/Δt=εΔΦE/Δt Q=CV=(εA/d)(Ed) Q=εAE...

Hi, I'm not sure if this is the right place for this...if it isn't if I could be redirected/if a moderator could move my post to the right place I would greatly appreciate it. In any case, I am trying to understand fractal dimensions. I read through wikipedia's description and I believe I...

Homework Statement Find the base and dimension of a system of equations: 3x1 - 5x2 + 2x3 + 4x4 = 0 7x1 - 4x2 + 1x3 + 3x4 = 0 5x1 + 7x2 - 4x3 - 6x4 = 0 2. The attempt at a solution Written in matrix form: 3 -5 2 4 7 -4 1 3 5 7 -4 -6 What I get: 11 -3 0 2 7 -4 1 3...

What is the dimension of a surface? My book says it's only 2-dimensional and I guess that makes sense because you only need two parameters to describe it. But other than that it's not really intuitive for me. I mean surely the shell of a sphere can't be vizualized in a xy-coordinate system only?

I am currently learning about volumes of revolution in calulus, and have looked ahead to surfaces of revolution as well. I want to try and extend this concept to revolving 3d functions over the x-axis into the fourth dimension. I found this thread...

HOw to calculate 3*x - x^2

I am participating in science project on behalf of my school. I am a 12th grade student and very much interested in Maths,Physics and Computer Science. My teacher has assigned me to do project on Multi Dimension i.e Fourth Dimension. I need some good stuff of resource and information on Fourth...

Is it possible for LQG to occur in higher dimension (more than 3+1)? If possible. How? If not possible. Do you notice LQG in fixed 4D compared to Strings 10D is pretty boring? Nature doesn't make sense for there to be 4D (3+1T) only when it could create more with no sweat. So this alone may...

I meet with a triangle integral where x+y≤1, and function is dependant only on x*y. I am wondering if there any possibility to relate ∫∫dxdyf(x*y)=∫d(x*y)f(x*y)g(x*y) or something similar? Or maybe there are some assumptions needed to relate like this?

Here is the situation I am concerned with - Consider a smooth curve g:[0,1] \to M where M is a topological manifold (I'd be happy to assume M smooth/finite dimensional if that helps). Let Im(g) be the image of [0,1] under the map g . Give Im(g) the subspace topology induced by...

Hi guys! I am getting some sort of contradiction using the definition of the killing-form. The killing form as a matrix (sometimes called metric) in some basis can be written as: \eta_{ab}=f_{ac}^df_{bd}^c where [ itex ] f_{ab}^c [ /itex ] are the structure constants of the Lie algebra. Of...

Homework Statement Show that the number of distinct solutions of a system of linear equations (in any number of equations, and unknowns) over the field Zp is either 0, or a power of p. The Attempt at a Solution First off, I was wondering whether there is any difference between...

a)since universe is expanding is today's 1 meter different from tomorrow's 1m? b)since distant between any 2 points is increasing is the universe expanding into 4th dimension?

How is it like to travel at the speed of light in the 4th dimension? and according to general relativity, the 4th dimension is time, what does that mean ?...and why? :rolleyes:

Hello all, Special relativity tells that space and time should be seen as a single four dimensional space time. Even the metric for SR has four components, x1, x2, x3, and x4 = ict. The Lorentz transform tells us how to convert these coordinates from this to another providing that we are...

Homework Statement Let V be the vector space of n × m matrices with entried in a field F . What is the dimension of V ? Give an explicit basis for V over F . The Attempt at a Solution The question is a little vague, but if I understand correctly, wouldn't the dimension of V simply be...

in the book of quantum mechanics concept and application by Zettili, chapter 4 write a theorem, that is: in one dimensional problem the energy level of a bound state system are discrete and not degenerate. i can not prove this theorem. can you help me to do this!

I think I may have asked this question a few years ago, but I forget the responses. We know that gravity is the curvature of spacetime in the presence of mass and energy.. The curvature of spacetime was proved by experiment during a solar eclipse, whereby light from a star behind the sun was...

A question about the average velocity of bodies undergoing one-dimensional motion and a constant acceleration (gravity in this case). A case scenario. Suppose that initially, I throw a stone into the air at a height h. For the sake of argument, let's suppose that even though I threw the...

Homework Statement given two matrices A, B of 5x5 order: \rho(A)<\rho(B) the nullspace for A is Sp{(0, 3, -1, 2, 1),(4, -2, 1, 4, 0)} prove that AB\neq 0Homework Equations \rho(A)=n- \rho(P_a)The Attempt at a Solution so I now that the nullity is 2 and so \rho(A)=3 and because of that 4\leq...

Alright, I have a kind of dumb question: Why do I distinguish between dq and dqi when considering the propagation from qi to q to qf? For example, if we want the wave function at some qf and tf given qi and ti, we may write: ψ(qf,tf)=∫K(qftf;qiti)ψ(qi,ti)dqi Why do we distinguish between dqi...

Well? Is there? And if there is what kind of experiment could I perform to prove that there is? Or prove that there isn't?

I made a code in assembly 8086. I load matrix (array) in memory with dimension 3x3. but this code works just for this dimension of matrix 3x3. Could someone give me an idea how could i make it to work with dimension m x n? the array is loaded in memory and at the end just print the result...

A projectile is shot horizontally at 220 m/s from the top of a 620 m high cliff. A) How long till the projectile hits the ground? B) How far from the base of the cliff does the projectile land? I am going to be honest. I have no idea how to do any of my Physics homework. ): I still...

Homework Statement V is a vector space with dimension n, U and W are two subspaces with dimension k and l. prove that if k+l > n then U \cap W has dimension > 0 Homework Equations Grassmann's formula dim(U+W) = dim(U) + dim(W) - dim(U \cap W)The Attempt at a Solution Suppose k+l >n. Suppose...

Greetings This is my first post in this section of PF. As the title says, I just want to know the typical dimensions of the two-slit experiment, intended for electron interference. That is, what are the slits made of, what is their spacing from the screen,source and from each other. Is...

Homework Statement A ball is thrown straight up. At the top of its path its instantaneous speed is a) 5m/s b) 20m/s c) 50m/s d) 10m/sHomework Equations The Attempt at a Solution

For what value of x, y, and z, will the equation P^x v^y T^z = constant, become Boyles law?

Is it to possible to use the special case of elastic collisions in one dimension with bodies that posses different mass. Ordinarily I know that if the body has same mass the velocity of the bodies will simply be exchanged but is the fact also hold for body with different masses? v_1 - v_2 =...

Hi there, does anyone knows the overall dimension for 2.5' hard disk drive?including all the components inside. who has the complete dimension? tq =)

Problem of the day: Trying to find the formula to use for my 15 year old daughter. A 20,000N car is parked on an incline that makes an angle of 30 degrees with the horizontal. If the maximum force the brakes can withstand is 12,000N, will the car remain at rest? She is just learning how to...

Let A be an n*n matrix. Consider the space span \{ I, A, A^2, A^3, ... \} . How would one show that the dimension of the space never exceeds n? I feel like the answer lies somewhere near the Cayley-Hamilton theorem, but I can't quite grasp it.

According to Nobel Prizer Steve Weinberg, there may a second dimension of time in the quantum realm. Instead of a particle being “spread out” occupying no address in space until the wave function is collapsed, it rather does have an address but not necessarily in our time. Is this possible? Can...

Hi, this is my first post, and I'm not an expert of any kind or do not believe I am. I have always been fascinated by science, but I some time ask myself some questions, here's one I don't seam to find much info. I found a lot of treads that mentioned the subject but nothing that actually...

Halo everyone, I am trying to consider a dice game using MATLAB. I used 'r=randi(6,a,b)' to get random number from MATLAB.Also run it for 200times.(a=a:1:x,b=b:1:y) Then used '[a,b]=mode(r)' to get the highest frequency value and add them together then put them in the table. For x=1 with y=1,2...

I was flipping through a physics text and some of the units seemed pretty 'crazy'. Just wanted to know if they can always be understood intuitively, like you can visualize what's going on e.g. force, mass x acceleration, if I look at it as kg*m/s^2 then it doesn't really make sense to me...

Homework Statement I have a problem trying to code these two programs, one is related to the obtain the fractal dimension of the Koch curve by using the method of the box counting dimension and also using the Grassberger-Procaccia algorithm Homework Equations For the box counting...

Homework Statement If we have ker(T)={0}, why is the dim(ker(T)) = 0? Does the 0 vector not count when determining the dimension? I thought the answer would be 1.

Homework Statement A stone is thrown downward with a speed of 18 m/s from a height of 11 m. (acceleration due to gravity: 9.81 m/s2) Your answers must be accurate to at least 1%. Give your answers to at least three significant figures. a) What is the speed (in m/s) of the stone just before...

Homework Statement A model rocket accelerates upward from the ground with a constant acceleration, reaching a height of 76 m in 7.2 s. What is the acceleration (in m/s 2)? What is the speed (in m/s) at a height of 76 m? Homework Equations V=Vo+at X=Xo+Vot+1/2at^2 V^2=Vo^2+2at(X-Xo)...

1. A pitcher throws a baseball at 60mph. How much time does it take the ball to reach the batter 50 ft away? 2.t = x/v 3. t = 50/60 t = 0.83

Homework Statement If VΩW contains only the zero vector, then dim(V+W)+dim(VΩW) = dim(v) + dim(W) becomes dim(V+W) = dim(v) + dim(W). Check this when V is the row space of A, W is the nullspace of A, and the matrix A is mxn of rank r. What are the dimensions? Homework Equations...

Homework Statement A 10.0g bullet is fired into a stationary block of wood (m=5.00 kg). The bullet imbeds into the block. The speed of the bullet-plus-wood combination immediately after the collision is 0.600 m/s. What was the original speed of the bullet? ball m=10.0g=0.01kg wood m=...