Dimension Definition and 881 Threads

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?

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...