Dimension Definition and 881 Threads

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...

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...

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=...

Prove that the space of 2×2 real matrices forms a vector space of dimension 4 over R. [12] Im unsure, anyone any idea?

Homework Statement 10. In reaching her destination, a backpacker walks with an average velocity of 1.34 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.68 m/s, due west, turns around, and hikes with an average velocity of 0.447 m/s, due...

Been stuck on this question for days and any help would be greatly appreciated A baseball going horizontally at 32.0 m/s [E] with a mass of 0.152 kg is hit by a bat for 0.002 seconds. the velocity after the ball after contact is 52.0 m/s [W 20 N] Find the impulse experienced by the ball...

a car starts from rest travels for 5.0s with a uniform acceleration of + 1.5m/s^2. The driver then applies the brakes, causing uniform acceleration of -2.0m/s^2. If the brakes are applies for 3.0s (a) how fast is the car going atthe end of the braking period and b how far has it gone I have...

A race driver has made a pit stop to refuel. After refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is 5.5 m/s^2; after 4.1 seconds he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant velocity of...

i know that line is a one dimension but i cannot understand then why do sometime need two spatial variable to specify the st line for example x+y=c is a straight line but we require two coordinates to define it then how it is one dimensional?

The lecturer said that a way to find the determinant of a matrix is to do the following det(A) = xdet(B) (1) where A is the original matrix, B is an arbirtray matrix and x is a scalar multiplier The lecturer also said that a simple way to find the determinant of a high...

Alright, I have wondered this for a very long time and probably thought about it for longer than I should have but the more I think about it, the more I seem to be correct and the more frustrating it is to talk to people about it... Anyways, I'm sure everyone has heard of the saying "lefty...

I'm moving on to my next section of work and i come across this example: Consider the homogeneous system x + 2y − z + u + 2v = 0 x + y + 2z − 3u + v = 0 It asks for a basis to be found for the solution space S of this system. And also what is the dimension of S. I know this might be...

Homework Statement A ball is thrown by Jed in the street and caught 2 seconds later by Jelo on the balcony of the house 15m away and 5.0m above the street level. What was the speed of the ball and the angle above the horizontal at which it was thrown? Homework Equations The Attempt...

Hello All, It's rather a simple question for advanced people. Consider a 3D Euclidean space: if one is given 2 points, a line can be build that goes through the points; for 3 points -- there is a plane. For 4D space: a line goes through 2 points and a hyperplane through 4 points...

Is it true that in 1+1 dimensional Minkowski spacetime scalar quantum filed theory defined by the lagrangian (in the interaction picture, so that the normal ordering makes sense): \mathcal{L} = : \frac{1}{2} (\partial_\mu \phi) (\partial^\mu \phi) - \frac{1}{2} m^2 \phi^2 -...

Please teach me this: Why in two dimension space many QTF theories become renormalizable.By the way,are there any relation between this and the world-sheet in string theory? Thank you very much in advance

Homework Statement Let F be a field. Prove that the set of polynomials having coefficients from F and degree less than n is a vector space over F of dimension n. Homework Equations The Attempt at a Solution Since the coefficients are from the field F, the are nonzero. So, if...

General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?

Hi. In the book I'm reading I've come to a question regarding degenerate states in one dimension. It says that in one dimension there are no degenerate bound states. But say I have a stationary state with some energy E, and assume that it is normalizable. You can easily show that the complex...

error 542, J appears in the dimension of a variable,yet is not a dummy argument,a variable available through USE or CONTAINS association,a COMMON variable,a PARAMETER,or a PURE FUNCTION the same error about I i am using i,j in order to point the temperature in length and time T(i,j) it is a...

What are the conditions for which it can be concluded that a system has discrete energy levels? For example a system in one dimension with the potential V(x)=b|x| has only a discrete spectrum. How I can prove it? My book says moreover that the energy eigenvalues have to satisfy the...

Hi, I was listening to Susskind's lecture on statistical mechanics (lecture 8). He mentioned in relation to Ising model of magnetized spin systems that there could not be any phase transitions in one dimensions. He mentioned that it has to do with the stability of the system. Can anybody...

I was thinking about the analogy of an observer living in a two dimensional world. So as it goes, this observer would see a 3d sphere as a 2d circle. As the 3d sphere moves through the dimension the observer cannot see, the circle would seem to appear on his plane from nowhere, grow to the...

In general, how do you define the dimension of a singularity? E.g., we think of a Schwarzschild singularity as pointlike, so that its world-line is one-dimensional, and on a conformal diagram we represent it as a spacelike line, which seems to make sense. In point-set topology, we have...

Homework Statement find the dimension of the linear span of the given vectors v1 = ( 2, -3, 1) v2 = ( 5, -8, 3) v3 = (-5, 9, -4) Homework Equations The Attempt at a Solution so all i did was make it a matrix and put it in rref and i got [1 0 0] [0 1 0] [0 0 1] does this...

Hi, I was not entirely sure where to post this, but I think this will work. With the gravitational field we have that g^{\alpha\beta}g_{\alpha\beta}=4 which is the dimension of the manifold I believe. I have normally heard of g_{\alpha\beta} being interpreted as the gravitational field...

Consider the space of all polynomials in n variables of degree at most d. The dimension of that space is C(n+d,d). How do I calculate the dimension of that same space when I restrict the domain of the polynomials to the unit ball? In that case all the polynomials (sum(i=1..n) x_i^2)^p with p a...

I was hoping you guys could help me in understanding some vector spaces of infinite dimension. My professor briefloy touched n them (class on linear algebra), but moved on rather quickly since they are not our primary focus. He gave me the example of the closed unit interval where f(x) is...

Homework Statement A boy throws a ball with v velocity upwards as well as downwards . What will be the displacement covered by the two balls if air friction and external force or viscosity is neglected ? Homework Equations According to me the equations of motions are relevant here ...

My definition of diffeomorphism is a one-to-one mapping f:U->V, such that f and f^{-1} are both continuously differentiable. Now, how to prove that if f is a diffeomorphism between euclidean sets U and V, then U and V must be in spaces with equal dimension (using the implicit function theorem)?

With normal vectors i usually check there is the correct number of vectors i.e 3 for R3 2 for R2 etc and then just check for linear independence but reducing the matrix that results from c1v1+c2v2+..cnvn=0 and determining of unique solution or infinite solutions. There are the right number of...

I have a question regarding constructing subway platforms in curved line. As we know, in a curve, wagons get out of linear alignment and become closer in inner radius and separate from each other in outer radius. I want to know the relation between dimension of car, dimension of structure...

This question will probably make the most sense to those who have read Edwin Abbott Abbott's novel Flatland. But I'm sure many others know the answer. To explain, I'll have to use some dimensional analogy. Let's say you're a 2-dimensional being. You live in a two dimensional world and thus...

Homework Statement Having a symmetric tensor S^{a_1 ...a_n} forming a vector space V_n with indices taking values from 1 to 3; what is the dimension of such a vector space? Homework Equations The Attempt at a Solution essentially this reduces to picking a tensor of type S^{...

can a function in ONE dimension have NO inverse ?? i mean if given the inverse function f^{-1} (x) = g(x) + \sum_{k=-N}^{k=N}c_{k}exp(ixlogk) the first function g(x) is an smooth function , the last Fourier series is a 'noise correction' t o this function g , N is a big but finite...

In http://arxiv.org/abs/1010.1939 Rovelli describes his present model as a generalized TQFT. The current quantum groups stuff is also strongly TQFT inspired (as spin foams in general are). This makes me wonder whether LQG should not in fact be "higher dimensional". The reason is that I've...