Dimension Definition and 881 Threads

Homework Statement Assume that e_1 ,..., e_n is a basis for the vector space V. Let W be the linear subspace determined (formed?) by the vectors e_{1}-e_{2}, e_{2}-e_{3}, ..., e_{n-1}-e_{n}, e_{n}-e_{1}. Determine the dimension of W, and a basis for W. Homework Equations The...

Find the dimension for the quantity c3 in the expression s=c3 cos (c4t). Please someone help me solve this, s is a distance with unit L, t is a time with unit T and theta is an angle in radians.

Homework Statement I am trying to find the domain of the following.. R^2 to R^3 of g(x,y) = (x-y,x+y,3*x) R^3 to R of h(x,y,z) = x/(y+z) Homework Equations The Attempt at a Solution I don't know how to start. I know how to find the domain in one dimension but how...

I read on a website (http://math.ucr.edu/home/baez/physics/Relativity/GR/gravity.html): "The world we live in consists of four dimensions, the three space dimensions and one that is not exactly time but is related to time (it is in fact time multiplied by the square root of -1)." In my...

information is a kind of "dimension" (like space and time) I always asked myself about how does information works in the cosmos. I read an article were some scientist told that information is a kind of "dimension" (like space and time), and its crucial for the conformation of systems (and...

Hey everyone, I'm not a physicist, I'm a high school senior with a who stopped taking math and science after sophomore year (which I sorely regret). So, I have a question rather than a crazy hypothesis regarding the primordial cocktail antecedent to the big bang that's dubious at best. Call...

in a space V^n, prove that the set of all vectors {v1,v2,..}, orthogonal to any v≠0, form a subspace V^(n-1). i know that a subspace of V^n must be at least one dimension less and the set of vector v1,v2,... build a orthogonal basis, but how can one show with this preconditions that the...

Hi, I need some hints for the proof of the sard theorem in 1 dimension: Prove that the set of critical values (f(x) where f'(x)=0) of continuously differentiable f:[a,b]->R has measure 0.My attempt:Fix \varepsilon, Let Crit(f) be the set of critical points of f. We want to show that...

let U and V be subspaces of Rn. Prove that dim(U+V)=dim U+dim V - dim(U∩V)

Dear guys, I read a derivation of the dimension of gamma matrices in a d dimension space, which I don't quite understand. First of all, in d dimension, where d is even. One assumes the dimension of gamma matrices which satisfy \{ \gamma^\mu , \gamma^\nu \} = 2\eta^{\mu\nu}...

Hey all. I know this is a basic concept but I don't really understand it. I don't get what the difference between rank and dimension is. According to my book, the rank of a matrix is the dimension of the column space. Does that not imply that they are the same, unless the question...

Right so I've had an argument with a lecturer regarding the following: Suppose you consider P_4 (polynomials of degree at most 4): A(t)=a_0+a_1t+a_2t^2+a_3t^3+a_4t^4 Now if we consider the subspace of these polynomials such that a_0=0,\ a_1=0,\ a_2=0}, I propose that the dimension of of this...

If mass influences the 'shape' of three dimensional space plus time, does that require a further or higher spatial dimension, or is that unnecessary?

Homework Statement Show that with d spatial dimensions the potential \phi due to a point charge q is given by \phi (r) = \frac{\Gamma(\frac{d}{2}-1)}{4\pi^{d/2}}\frac{q}{r^{d-2}} Homework Equations The Attempt at a Solution The electric field strength is known to be: E(r) =...

I have a vector of all ones in n-dimensions. For example (1,1,1) in 3D. I want to find a invertible rotation matrix T that transforms the vector of all ones to the vector (0,0,0,...,0,,1): Let v be the vector of all ones, and w=(0,0,...,0,1) Find T such that T.v == wIn low dimension it is easy...

IF consciousness is a result of complex physical processes, and could thus be simulated by a hugely complex computer program (which should not be extremely controversial) - WHAT IF the finite execution of the computer program would be presented, not with temporal steps (using the time...

Hi! I am working on the following problem: If a matrix is antisymmetric (thus A^T = -A), show that P = {A \in R | A is antisymmetric} is a subset of Rnxn. Also, find the dimension of P. So far, I've proven that P is a subset of R and I am guessing that, in order for me to find the...

Homework Statement First of all sorry if my terminology sounds a bit weird, i have never studied mathematics in english before. So this is the problem: We have the space R^2x2 of all the tables with numbers in R. We also have a subspace V of R^2x2 of all the tables with the following...

Just a quick question. I know that it is pretty much taken to be axiomatic, but is time a testable dimension?

Homework Statement 1. A particle of mass m is constrained to move along a straight line. In a certain region of motion near x = 0 , the force acting on the particle is F = -F_0 sin(bx) , where F_0 and b are positive constants. (a) Find the potential energy of the particle in this region...

Homework Statement Particle 1 of mass m1 = 0.30 kg slides rightward along an x-axis on a frictionless floor with a speed of 2.0 m/s. When it reaches x = 0, it undergoes a one-dimensional elastic collision with stationary particle 2 of mass m2 = 0.40 kg. When particle 2 then reaches a wall...

Homework Statement Block 1 of mass m1 slides along an x-axis on a frictionless floor with a speed of 2.40 m/s. Then it undergoes a one-dimensional elastic collision with stationary block 2 of mass m2 = 2.00m1. Next, block 2 undergoes a one-dimensional elastic collision with stationary block...

Hello there, i wanted to know what is the difference between a surface in R^2 and a surface in R^3 in an xyz cordiante system. More specifically how do they look like? an example please. Is this different from a 2 dimensional surface and a 3 dimensional surface respectively. Also what...

I've often heard that time was considered a dimension, but I don't understand how this is possible as it invalidates the idea of motion. Take a simple number line for example. This is considered the first dimension. A point can be at any place on said number line. Moving on up to the second...

Homework Statement A cart with mass 310 g moving on a frictionless linear air track at an initial speed of 1.4 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision, the first cart continues in its original direction at 0.64 m/s...

Can anyone help me with a problem. Please just answer whatever you can. Thanks. I have not started the problem because I don't know where to begin. I can solve physics problems but i just can't seem to start any of them off. A classical particle of mass m moves in the presence of the...

This is not a homework problem, I am not sure what section to put this (I apologize if it's in the wrong place). So I take AP Physics B at my high school and we just got our first test back on Kinematics in One Dimension and I got a 53%! I know that might sound horrific (which it is) but my...

A rock is dropped from rest into a well. The sound of the splash is heard 2.40 s after the rock is released from rest. a)How far below the top of the well is the surface of the water? The speed of sound in air (at the ambient temperature) is 336 m/s. (b) What If? If the travel time for...

Homework Statement A car starts from rest at a stop sign. It accelerates at 4.0 m/s^2 for 6.0 s, coasts for 1.9 s, and then slows down at a rate of 3.0 m/s^2 for the next stop sign. How far apart are the stop signs? Homework Equations The Attempt at a Solution

Homework Statement It's a two-part problem, the first part was deriving a Schrodinger equation from when x = r cos(theta) and y = r sin(theta) I got: -\frac{\hbar^2}{2m}[\frac{\partial^2}{\partial...

Hi. I am new to Physics Forums. The following problem is from Physics 6th Edition by Cutnell/Johnson. A hot air balloon is rising upward with a constant speed of 2.50 m/s. When the balloon is 3.00 m above the ground, the balloonist accidentally drops a compass over the side of the balloon...

Homework Statement Determine the stopping distances for an automobile with an initial speed of 90 and human reaction time of 1.0 : (a) for an acceleration = -5.0 , (b) for = -7.5 . Homework Equations vf = vo + at avg velocity = (vf + vo) /2 d = vo)t + (1/2) at2 vf2 = vo2 + 2ad...

Homework Statement An unmarked police car traveling a constant 85 is passed by a speeder. Precisely 1.00 after the speeder passes, the police officer steps on the accelerator. If the police car accelerates uniformly at 3.00 and overtakes the speeder after accelerating for 5.00 , what was the...

Homework Statement A rocket starting at rest takes on a net acceleration of 20m/s^2 in a vertical line until it runs out of fuel after 5 seconds. At what height does it run out of fuel? What is its velocity when it runs out of fuel? What is its maximum height? How long does it take to hit the...

I have a few problems I'm having trouble with. If I can get some help with this one I should be able to figure out the rest I have. 1. A rock is thrown downward from the top of a tower with an initial speed of 12 m/s. If the rock hits the ground after 2.0 s, what is the height of the tower...

is it time? what's your theory on the study of other dimensions? and applications from them?

I have read speculations that (1) the cosmic microwave background radiation has a fractal distribution (non-integral Hausdorff dimension), and (2) the same might be true of galaxy cluster distribution (although different dimensionality to (1)) Whether or not one or both analyses are...

Homework Statement For each quantity listed, indicate dimensions using mass as a primary dimension and give typical SI and English units: power pressure modulus of elasticity angular velocity Homework Equations The Attempt at a Solution im not sure i understand what it is...

Hi, I was wondering how the state vector for a particle in a 1-D box can be expanded as a linear combination of the discrete energy eigenkets as well as a linear combination of the continuous position eigenkets. It seems to me that this is a contradiction because one basis is countable whereas...

Homework Statement A ball is thrown upward from the top of a 25.0-m-tall building with an initial speed of 12m/s. At the same time, a person is running on the ground at a distance of 31.0m from the building. What is the person's average speed if he catches the ball at the bottom of the...

Homework Statement Two motorcycles are traveling due east with different velocities. Four seconds later, they have the same velocity. During this 4s interval, motorcycle 1 has an average acceleration of 2.0 m/s(squared) due east, while motorcycle 2 has an average acceleration of 4.0...

Homework Statement A Pendulum weighs .5kg and has a string length of 70cm swings from a horizontal position downwards to hit a block that weighs 2.5 kg and is on a frictionless plain. Calculate the speed of both the ball and the block after the elastic collision. Homework Equations...

Homework Statement Prove that if W is a subspace of an n-dimensional vector space V and dim(W) = n, then W=V Homework Equations The Attempt at a Solution I don't know where to start.

Homework Statement Find an example of subspaces W1 and W2 in R^3 with dimensions m and n, where m>n>0, such that dim(intersection of W1 and W2)= n Homework Equations dim(W1+W2)= dim(W1) + dim(W2)-dim(intersection of W1 and W2) The Attempt at a Solution Well what I know...

Homework Statement "2 cars C and D travel in the same direction in straight line. During particular time interval t, car D is AHEAD of car C, and D is speeding up while car C is slowing down. During the interval t, it is observed that the distance between the cars decreases. Explain how this...

In my course I am curios to know how the dimension of angle becomes [LL^-1]. The following pic is taken by course book. http://i42.tinypic.com/iy2y3r.jpg

Since when is Time considered to be a dimension? Is it after Einstein's G.T.R. or was it considered to be one before it?

Homework Statement Suppose that dim V = m and dim W = n with M>=n . If the linear map A : V -> W is onto, what is the dimension of its kernel? Homework Equations The Attempt at a Solution Onto, means that every vector in W has at least one pre-image therefore, the kernel can...

Homework Statement Is the collection a subspace of the given vector space? If so what is the dimension? V={ax^2+bx+c: a=b+c} in P2 Homework Equations The Attempt at a Solution The first part of the question is pretty straightforward. I just verified closure under addition and...

Homework Statement Heather and Jerry are standing on a bridge 46 m above a river. Heather throws a rock straight down with a speed of 30 m/s. Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance. How much time elapses between the...