Dimension Definition and 909 Threads

According to the link below, fractal dimension is an exponent of some sort: http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html The Hausdorff Dimension (aka fractal dimension) is denoted as D in the website above. And r is the base number. If we were to look at...

Can not figure out my ? Subscripted assignment dimension mismatch-problem EDIT: This is Matlab code. Hello! I have some MATLAB code and I've run into a problem that I can't seem to be able to solve. I hope that someone might help me find a solution. Here is the error ? Subscripted...

HI! Everyone!I have a problem! I read sakurai's <modern quantum mechanics>.It reads the dimension of <xn,tn|xn-1,tn-1> is 1/length.I DON'T understand!would you like to give me some explanations? thank you!

Hi guys I m new to his forums o I hope I post this in the right place. I have a questions about the 11 dimension. As I saw some documentaries about M theory, it seems our universe was created by colision in the 11 dimension. So I was wondering how does it looks like. At the beginning of big...

Objective questions regarding "projectile motion - 2 dimension". Homework Statement There are 2 mini problems : 1. If t1 and t2 be the times of flight from A to B and "θ" be the angle of inclination of AB to the horizontal , then t12 + 2t1t2sinθ + t22 is (A.) independent of θ (B.)...

I have a project where I need to solve T''(x) = bT^4 ; 0<=x<=1 T(0) = 1 T'(1) = 0 using finite differences to generate a system of equations in Matlab and solve the system to find the solution So far I have: (using centred 2nd degree finite difference) T''(x) = (T(x+h) - 2T(x) +...

For an arbitrary distance the equation is: \sqrt{\Sigma_{i}^{n}x_{i}^{2}} I would like to know what are the proofs for higher dimensions being perpendicular to our 3-spaital dimensions. If I am wrong in any way, please elaborate. I guess what I'm saying is since: r^{2}=x^{2}+y^{2}...

Homework Statement Let W be the subspace of R4 defined by W={x:V^TX=0}. Calculate dim(w) where V=(1 2 -3 -1)^T note: V^T means V Transpose, sorry I don't know how to do transpose sign in here. Homework Equations The Attempt at a Solution I tries to do it (1 2 -3 -1)(x1 x2 x3...

Why is the unit vector for time in Minkowski space i.e. the fourth dimension unit vector always opposite in sign to the three other unit vectors? The standard signature for Minkowski spacetime is either (-,+,+,+) or (+,-,-,-). Is there some particular reason or advantage for making time...

Which is the mass dimension of a scalar filed in 2 dimensions? In 4 dim I know that a scalar field has mass dimension 1, by imposing that the action has dim 0: S=\int d^4 x \partial_{\mu} A \partial^{\mu} A where \left[S\right]=0 \left[d^4 x \right] =-4 \left[ \partial_{\mu} \right]=1...

Hi Could someone tell me if Higgs bosons exist in another dimension or if there's simply something i don't understand about their existence in our timespace? Meaning - from what I understand - the recent experiments at the LHC smashed together particles with enough energy to create a Higgs...

Exercise #17 in Linear Algebra done right is to prove that the dimension of the direct sum of subspaces of V is equal to the sum of the dimensions of the individual subspaces. I have been trying to figure this out for a few days now and I'm really stuck. Here's what I have got so far: Choose...

Hey guys, Does anyone have a list of the maximum dimensions of objects that can be carried in various launch vehicles, eg Falcon 9/Falcon Heavy, space shuttle etc? It would be much appreciated!

Homework Statement Homework Equations The Attempt at a Solution Does the Christoffel symbol \Gamma have a dimension in physics? And if it does, what is its dimension? Thank you!

Multi-Variable / Dimension Fourier Decomposition Say we have f(x, y). We can Fourier decompose it in terms of f1(y, v) and e^{\ x\ v}, f2(x, u) and e^{\ u\ y}, or both variables simultaneously f3(u, v) and e^{\ x\ v\ +\ u\ y}. Similarly for any greater number of variables or dimensions. Now, is...

Homework Statement The velocity of particle is 0 at t=0. Then , (a) The acceleration at t=0 must be zero. (b) The acceleration at t=0 may be zero. (c) If the acceleration is 0 from t=0 to t=10 s , the speed is also zero in this interval. (d) If the speed is 0 from t=0 to t=10 s...

Not sure if its the right place to post but still:- I am confused over 4th dimension space( not time ). Does 4th dimension space really exist? If it exists why we cannot see or visualise the 4th dimension?

Homework Statement V = {p(x) belongs to P3 such that p'(1) + p'(-1) = 0} Homework Equations ... The Attempt at a Solution Okay, so finding the first derivative of p(x) = ax^3 + bx^2 + cx + d and plugging in the values 1 and -1 (to find p'(1) and p'(-1)), we get c = -3a. Does this make the...

Homework Statement A= \begin{bmatrix}1 & 1 & 1 & 1 \\ 2 & 1 & 0 & -1 \\ 3 & 4 & 5 & 6 \\ -1 &2 &1&0 \end{bmatrix}Determine the dimension of A and give a set of basis vectors for A. Homework Equations Dimension of matrix, ref form of matrix. The Attempt at a Solution I reduced the...

I am becoming confused when I read in Wiki that the dimension of the circle in the plane is 1! It is said that the dimension of circle is 2 (in general )! I do not get it!

I know the topic of time has been brought up on multiple threads, and they are interesting. But I would like to ask the question a bit differently than I've seen it asked. When I took Physics 1A the instructor basically said that Einstein showed that time was an independent variable, then...

Hi. 1. Can anyone definitively tell me what the dimension formula for the classical Lie algebras? For example, I know for SO(2n) or D_n, the dimension formula is SO(N)--> (N*(N-1))/2 E.g. SO(8) is 8*7/2 = 28. Ok, so what about SU(N+1) i.e. A_n, SO(2n+1) i.e. B_N and Sp(n) i.e...

How can i solve Schrodinger equation in 3dimension i want to know how can i deduce every equation ? and how can i find equation of spherical harmonic and radial equation ? i need to understand this proof

[b]1. The problem statement, all variables and given/known A general one dimensional scattering problem could be characterized by an (arbitrary) potential V (x) which is localized by the requirement that V (x) = 0 for |x|> a. Assume that the wave-function is ψ (x) =  Ae^(ikx) + Be^(-ikx)...

If we consider the set R of all linear transformations from an p-dimensional vector space Z to Z (T:Z -> Z), what do we know about the dimension of the set R? In other words, what do we know about any basis for R? What are its properties?

Is it possible?

I wanted to know what is the definition and what actually is a dimension. I mean I get that length, width and height story, but how does time fit in as a dimension. Then what about higher dimensions. Like if a certain system was defined in 7 dimensions what exactly would those dimensions be? 4...

To start, let's say I took a bowling pin and passed it through a two-dimensional universe. An observer in the two-dimensional universe would see a two dimensional slice of the bowling pin expanding and contracting as the bowling pin passed through their universe. Similarly, a 4-dimensional...

I'm a little confused about some of the matrix terminology. I have the following subspace: span{v1, v2, v3} where v1, v2, v3 are column vectors defined as: v1 = [1 2 3] v2 = [4 5 6] v3 = [5 7 9] (pretend they are column vectors) How am I supposed to find the dimension of the span? My...

Find dimension and ker of matrices ?? Let V be an F-vector space and (phi:v->v) be an F-linear transformation of V . Define what it means for a vector v ε V to be an eigenvector of phi and what is meant by the associated eigenvalue. This is the form of the question during my calculations I...

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?