Dimension Definition and 881 Threads

Check whether the following are subspaces of $\mathbb{R}^3$ and if they're find their dimension. (a) $$x = 0$$, (b) $$x+y = 0$$, (c) $$x+y+z = 0$$, (d) $$x = y$$, (e) $$x = y= z$$, and (f) $$x = y$$ or $$x = z$$. (a) Let $S = \left\{(x, y, z) \in \mathbb{R}^3:x = 0 \right\}$. I want to check...

The power law of Coulomb depends on the dimension treated . It is $$1/r^{n-1} $$ where n is the dimension. In n=3 we get the inverse square law. How does this go into considering now spacetime 3+1 dimensional ? Would it modify the law and how ?

Homework Statement Let U is the set of all commuting matrices with matrix A= \begin{bmatrix} 2 & 0 & 1 \\ 0 & 1 & 1 \\ 3 & 0 & 4 \\ \end{bmatrix}. Prove that U is the subspace of \mathbb{M_{3\times 3}} (space of matrices 3\times 3). Check if it contains span\{I,A,A^2,...\}. Find the...

Homework Statement I know some people use R to mean all numbers in only one dimension which span a line. R^2 meaning numbers with two dimensions that span a plane. R^3 meaning three dimensional numbers that span three dimensional space. I'm not really sure if I worded that correctly but I think...

Hello, Can you tell me what is the difference between direction and dimension?

Homework Statement A particle with mass m and electric charge e is confined to move in one dimension along the x -axis. It experiences the following potential: V(x) = infinity when x<0, V(x) = -e^2/4*pi*ε*x when x≥0 For the region x ≥ 0 , by substituting in the Schrödinger equation, show that...

Is not space curvature the curving or projecting into a higher dimension? Like a curved sheet of paper perceived by a two dimensional creature? The mystery seems to reside in our ape brains being unable to perceive (but not conceptualize) higher dimensions than three or relativistic, quantized time.

1. Homework Statement I'm taking a swing at Spivak's Differential Geometry, and a question that Spivak asks his reader to show is that if ##x\in M## for ##M## a manifold and there is a neighborhood (Note that Spivak requires neighborhoods to be sets which contain an open set containing the...

Dear all, If we consider the lagrangian to have both geometric parts (Ricci scalar) and also a field, the action would take the form below: \begin{equation} S=\frac{1}{2\kappa}\int{\sqrt{-g} (\ R + \frac{1}{2} g^{\mu\nu} \partial_\mu \phi \partial_\nu \phi -V(\phi)\ )} \end{equation} which are...

Hi all, I know that the dimension of a partial decay width or a cross section should be GeV or pb respectively. But what if i have a decay width probational to ## \Gamma = 10^{-3} GeV^3 G_\mu ## where I calculated all the masses and constants in ## \Gamma ##, ## G_\mu ## is the Fermi...

Dimension of Phase Space of a rigid diatomic molecule is 10. Shouldn't it be 12?

Could you use the formula "planck length/c=planck time" to convert time into a spatial distance? Using that to tell how far something is through time.

Homework Statement Find basis and dimension of V,W,V\cap W,V+W where V=\{p\in\mathbb{R_4}(x):p^{'}(0) \wedge p(1)=p(0)=p(-1)\},W=\{p\in\mathbb{R_4}(x):p(1)=0\} Homework Equations -Vector spaces The Attempt at a Solution Could someone give a hint how to get general representation of a vector...

Hi, I need to write a subroutine that accepts as an argument an array of any number of dimensions, where each dimensions has any size. The array is contiguously allocated. In C, I can do this pretty cleanly. void array_func(int ndims, int *dims, int *array) { // do stuff with...

Mod note: Moved from Precalc section 1. Homework Statement Given l : IR3 → IR3 , l(x1, x2, x3) = (x1 + 2x2 + 3x3, 4x1 + 5x2 + 6x3, x1 + x2 + x3), find Ker(l), Im(l), their bases and dimensions. My language in explaining my steps is a little sloppy, but I'm trying to understand the process and...

Hello, I have recently been very interested in learning about the 4th dimension (well the little we know about it) I have listened and discussed in some conversations about the topic and have a few thoughts and it questions. -From my understanding the Tesseract is a 3rd dimensional Shadow...

I have function1: x = n(cos((pi/2)-2pi/n)) and function2: y = n(sin((pi/2)-2pi/n)) my goal is to plot a graph where for the same value of n, the x and y are respectively the horizontal and vertical component of the point, this graph should preferably possible to create on a computer or a...

This thread is also my introduction to the forum, so hello. So the basic setup of my story is the hordes of hell invade New York City. I'm agnostic, so it's more "beings from another dimension enter ours" than a religious thing - it's like the DOOM game series. Let's say that a certain amount...

The generators of ##SO(n)## are pure imaginary antisymmetric ##n \times n## matrices. How can this fact be used to show that the dimension of ##SO(n)## is ##\frac{n(n-1)}{2}##? I know that an antisymmetric matrix has ##\frac{n(n-1)}{2}## degrees of freedom, but I can't take this idea any...

4rth/5th coordinate?* Hi, I'm just wondering: if there is an entity in space, which can be located with Cartesian coordinates in the 3 dimensions of say, 2 right (from a seemingly arbitrary reference point), 2 up, and 2 forwards, then at this point (2, 2, 2), an entity could also be spinning at...

Hello everyone. I have a question about compressive strength of concrete. It is said that (in my country) 150 mm x 150 mm x 150 mm concrete cube is used for concrete testing. Someone asks me why 100 mm x 100 mm x 100 mm is not used. In fact, I know that sometimes it is allowed or even preferred...

So the theorem says: Suppose that ##U## and ##V## are finite dimensional vector spaces, and that ##T:U\to V##, ##S: V \to W##. Then ##\text{dim Ker }ST \le \text{dim Ker }S + \text{dim Ker }T##. Proof: Set ##U_0 = \text{Ker }ST## and ##V_0 = \text{Ker }S##. ##U_0## and ##V_0## are subspaces of...

My linear algebra is a bit rusty. Let ##A=\{\bar{v}_1, \dots, \bar{v}_1\}## be a set of vectors in ##R^n##. Can dim(span##(A))=n## without spanning ##R^n##? I guess I'm unclear on how to interpret the dimension of the span of a set of vectors.

String Theory speculates that extra dimensions may exist. Obviously, it would be difficult to describe or imagine that, but is it possible that there are objects or particles that exist observing LESS dimensions. For example, photons travel at c meaning that time travels infinitely slow in for...

Hey guys! After watching another awesome video of minutephysics: I couldn't help but wonder, what is a dimension? Thanks for your replies in advance,

Hi guys, I was wondering if anybody could help me understand the concept of spacetime. My physics knowledge is quite limited but so far what I have gathered is: Spacetime is like a piece of paper (assuming it is 2d) but instead of width and length it has space on one axis and time on another...

I think it's 3... All 2x2 can be written as a_1 A_1 + a_2 A_2 + a_3 A_3 + a_4 A_4 with A_1 = \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix} , A_2 = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} , A_3 = \begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix} , A_4 = \begin{bmatrix} 0 & 0 \\ 0 & 1...

Hi, I wanted to know if the endpoints of an nth dimension linear equation will be guaranteed to contain a min and max over that interval. For 1D ( like a line), if I find f(x) over an interval [x0, xn], I'm guaranteed that the two end points will be either an max or min. So I was wondering if...

Homework Statement Hence no one in the science section helped me I decided to come here. Anyways, the problems are just basic math.[/B] 1 )A gallon of gasoline carries with it about 1.3*10^8 J of energy. Given a price of $3 per gallon, how many Joules can you get for a dollar? 2)Electricity...

Homework Statement Is the following equation dimensionally correct? Homework Equations E = (1/2) mv where: E = energy m = mass v = speed The Attempt at a Solution 1. I understand that the 1/2 is irrelevant. 2. I broke everything down into length, time, and mass. 3. I got ML^2/T^2 = ML/T 4. My...

What is the fourth dimension can anybody explain it to me ?

Hello. I am not familiar with differential geometry and curvature tensors, yet I am having a great deal of questions to ask. First when we lay a set of coordinates for an n-dimensional plane, let's say 2 coordinates for a surface embedded in a 4D space the vectors we begin with to describe our...

Hello and first of all I would like to say that I appreciate your work here since I am new to this forum. So here it goes. I was wondering for a long time. Someone travels back in time somehow and let's say he goes 1000 years back. He knows the future and he makes an action to change it. Our...

I want to know which dimension does the black hole belongs? Can anyone say which force is responsible for the absorption? In case, if the black holes absorbs everything then were the things might gone?Is that everything becomes invisible or just blast into pieces?

Hi, I have a problem with a code I'm working with. I'm a student in physics and I'm writing a code in Fortran 90 that should calculate the Polonium's half-life time. I have no data to work with so I generated them with the library random number and here is the problem, I have a 300 lines code...

Some people say that it's the 3D world we live in + time but others say that it's 4 dimensional as in it as new axis. Which one is true?

The coefficient of the stress energy tesor in the GR equation reduces to 8π/Ν, where N = {"(Kg)m/s^2.} Is it correct to conclude that all the elements of the stress energy tensor must have the dimension of N = (Kg)m/s^2 since the curvature and metric tensors on the other side of the equation are...

if we do picard's iteration of nth order linear ODE in the vector form, we can show that nth order linear ODE's solution exists. (5) (17) example) (21) (22) (http://ghebook.blogspot.ca/2011/10/differential-equation.html)I found that without n number of initial conditions, the solution...

Like spacetime , can sound be taken as a fifth dimension?

Hey guys, I'm a newbie here. Is it true that one could understand fifth and above dimensions only if we get hold of fourth dimension and I've seen videos and read about fourth dimension but couldn't get it completely and exactly. So, I want your help here. Be mellow as much as you can. Thank you.

I have read that the elementary particles of the Standard Model have dimensions 0. Is this the case or not? I have read on this site relevant answers to similar questions, but have not found them to be very clear. If it is the case, surely much of quantum weirdness is thereby explained: after...

The problem statement. When an exercises say " the interaction in a QFT has dimensions Δ" , what does it mean?, it means the field or the Lagrangian has this mass dimension? In this exercise I'm trying to find the classical beta function (β-function) for the assciated couling.

I am attaching a picture of a proof from the book "general relativity" by wald. This is supposed to show that the tangent space of an n dimensional manifold is also n dimensional. I have two questions. In equation 2.2.3 couldn't the function be anything at a since the (x-a) term is 0? How is...

James walks 2 km away from home in 30 minutes. He then turns around and walks back home along the same path, also in 30 minutes. Calculate James’ average speed and average velocity. My answer: s = d / t = 4000m / 3600s = 1,11 m.s -1 v = Δx / Δt = 0 m / 3600 s = 0 m.s-1I'm just...

Hi people. I just read some articles about physicist starting to gain more and more evidence for the Universe to be a 3D Hologram of a 2D world (or that's how I understood it). And apparently for us living in a "Matrix", like the one in the movie. Now I would like to understand the relation...

Hi, apologies for the length of this, I'm hoping as a group you knowledgeable established or future Engineers and Physicists can help me out with a problem. I have been having a discussion with a colleague about expansion of a 6m x 7m integrally waterproofed (Kryton KIM) concrete slab roof that...

Homework Statement A. Let {t,u,v,w} be a basis for a vector space V. Find dim(U) where U = span{t+2u+v+w, t+3u+v+2w, 3t+4u+2v, 3t+5u+2v+w} B. Compute the dimension of the vector subspace V= span{(-1,2,3,0),(5,4,3,0),(3,1,1,0)} of R^4Homework EquationsThe Attempt at a Solution I know that...

Homework Statement Find the probability distribution for a random walk on a d-dimensional lattice.[/B]Homework Equations [/B]The Attempt at a Solution I'm trying to find the probability distribution for a random walk on a lattice with lattice constant a in arbitrary dimension d. The rules...

While I'm reading a book in quantum mechanics, I reached the part "Generalization to infinite dimension". We know that at infinite dimension many definitions changes.And that what is confusing me! Take for example the inner product.when we are dealing in finite dimension the definition of inner...

Homework Statement Let ##\langle\psi| = \int^{\infty}_{-\infty}dx\langle\psi|x\rangle\langle x|.## How do I calculate ##\langle\psi|\psi\rangle?## Homework Equations ##\int^{\infty}_{-\infty}dxf(x)\delta(x-x_0)=f(x_0)## The Attempt at a Solution ##\langle\psi|\psi\rangle = \int\int...