Dimension Definition and 881 Threads

Hi! It's been like two days since I have tried to make this work, still I got nothing. Searched Google etc. but no help there. I have a three dimensional matrix in form of {{a,b,c}, {d,e,f}, {g,h,i}, ... etc. } with a total of 51 elements, i.e. 51x3 matrix. What I want is to plot it as...

Box counting dimension! please help! Hi all, I am working on a problem from Chaos theory, I have to find the box counting dimension of the set {0}U{n^-p} where n is an integer and p>0. I started this problem by considering p=1. So, the set looks like {0,1,1/2,1/3,...}. If I take intervals...

Please help to find the dimension that will maximize...? The Park Service is building shelters for hikers along the Appalachian Trail. Each shelter has a back, a top, and two sides. Find the dimensions that will maximize the volume while using 384 square feet of wood. length (across the...

For SU(2) the three represented gauge fields are A_\mu^1, A_\mu^2 and A_\mu^3 and for U(1) the gauge field is B_\mu. The A_\mu^3 and B_\mu are electrically neutral. The photon \gamma and Z particle are combinations of these. My interest is the dimensions of the following parameters...

"Spacetime has No Time Dimension" http://www.dailygalaxy.com/my_weblog/2011/04/spacetime-has-no-time-dimension-new-theory-claims-that-time-is-not-the-4th-dimension.html#more

Soft Article: http://www.sciencedaily.com/releases/2011/04/110420152059.htm Journal Article: http://prl.aps.org/abstract/PRL/v106/i10/e101101

I need some help with the equation of moments for this exercise: Each wheel of an automobile has a mass of 22 kg, a diameter of 575 mm, and a radius of gyration of 225 mm. The automobile travels around an unbanked curve of radius 150 m at a speed of 95 km/h. Knowing that the transverse distance...

I was given this question as a study question but no solution provided. I am unsure how to solve the question. Homework Statement A man is swimming 3m/s down a river. The man is 50m from the edge and 1000m from the top of the river. If I am in a boat at the top corner of the river...

Homework Statement If V and W are 2-dimensional subspaces of \mathbb{R}^{4}, what are the possible dimensions of the subspace V \cap W? (A). 1 only (B) 2 only (C) 0 and 1 only (D) 0, 1, 2 only (E) 0,1,2,3, and 4 Homework Equations dim(V + W) = dim V + dim W - dim(V \cap W) dim (V + W) \leq...

Hi, I had a question about understanding some basic thing about the Hausdorff dimension. Specifically, I'm trying to understand why the two dimensional Hausdorff dimension of a 1-d line is zero. In terms of the two dimensional Lebesgue measure, I can see that I can cover the line by a...

Homework Statement x=ut- y^{2} * z^{2} / V x,y,z is length u is speed t is time V is volume The Attempt at a Solution m = m/s * s - (m^{2} * m^{2} / m^{3}) m=m- m^{4}/m^{3} m=m-m m=0 there is inconsistent? is this correct?

1.I am busy with an assignment based on a Vibration experiment in a Mechanical Engineering degree program The procedure is documented in the lab handout and one part is to compare the measured natural frequency to the calculated natural frequency The formula given in the handout for natural...

I have a similar question about rotation matrices. I'm trying to understand the dimension of the matrix given below which is a 3-D rotation. I think that its dimension is 3 but unsure. Any help appreciated. Thanks, John [(cosx sin x 0), (-sinx cosx 0), (0 0 1)] with ( ) = row,

Two bodies begin a free fall from rest from the same height. If one starts 1.0 s after the other, how long after the first body begins to fall will the two bodies be 10 m apart? x = x + vt +1/2at^2 I'm having trouble visualising a solution.

Is the 4th dimension time? 0D = dot 1D = line 2D = plane 3D = sphere 4D = time Am I correct?

Homework Statement Find a basis for each of the spaces and determine its dimension: The space of all matrices A=[a b, c d] (2x2 matrix) in R^(2x2) such that a+d=0 Homework Equations The Attempt at a Solution So I jumped at this question without knowing too much about spaces and...

Homework Statement 1. Consider three linearly independent vectors v1, v2, v3 in Rn. Are the vectors v1, v1+v2, v1+v2+v3 linearly independent as well? 2. Consider a subspace V of Rn. Is the orthogonal complement of V a subspace of Rn as well? 3. Consider the line L spanned by [1 2...

Homework Statement The mass of a van with a driver is 2000 kg . When the van accelerates, the velocity increases with a uniform acceleration of 3.0 m/s2. Homework Equations a) The van starts at rest. Find the velocity after 4.0 s. b) How far does the van travel in the first 4.0 s? c)...

Homework Statement Prove that if A: V - >V is a linear map, dim V = n, and h1,...,hk (where 1,...,k are subscripts) are pairwise different eigenvalues of A such that their geometric multiplicities sum to n, then A does not have any other eigenvalues. Homework Equations Note sure if this is...

Homework Statement A rocket is launched from level ground with a speed of 30.0 m/s at an angle of 40 degrees above the horizontal. Find: a) Maximum height reached by the rocket. b) The time rocket is in the air. c) the horizontal distance where the rocket lands. Homework Equations...

Homework Statement Here is the problem verbatim (values have been slightly changed, also assume a frictionless environment): "A 4.3 kg block A and 6.0 kg block are connected by a string of negligable mass. Force FA = (15 N) acts on block A; force FB = (24 N) acts on block B. What is...

Homework Statement let V be a finite dimensional vector space of dimension n. For W \leq V define the codimension of W in V to be codim(W) = dim(V) - dim(W). Let W_i, 1 \leq i \leq r be subspaces of V and S = \cap_{i=1}^{r}W_i. Prove: codim(S) \leq \sum_{i=1}^{r} codim(W_i)Homework...

Homework Statement Two spacecraft are 13,500m apart and moving directly toward each other. The first spacecraft has in initial velocity of 525 m/s and accelerates at a constant -15.5 m/s^2. They want to dock, which means they have to arrive at the same position at the same time with...

Let A = k[x,y,z] and Y = \{(t,t^2,t^3)|t \in k\}, which is irreducible. It corresponds to the prime ideal p=(y-x^2,z-x^3). A(Y) is generated by x,y,z of degree 1 as a k-algebra in its graded ring structure. Each group corresponding to the degree d is spanned by the linearly independent...

Hi all The impulse response h(t) of an electric circuit (maybe in some special cases) is the derivative of the step response s(t) of the same circuit. right? So does it mean they have different dimension, namely if the dimension of s(t) is X, then the dimension of h(t)=ds/dt is x over...

Hi, I'm having trouble understanding a proof of the following theorem which allows it to be shown that all bases for a vector space have the same number of vectors, and that number is the dimension of the vector space (as you probably already know): Homework Statement Theorem: If S =...

First of all I would like to wish a happy new year to all of you, who have helped us understand college math and physics. I really appreciate it. Homework Statement Determine the dimension of the image of a linear transformations f^{\circ n}, where n\in\mathbb{N} and...

hi, what do you think that in general relativity, since space is curved, the curvature could be interpreted as a 4th space dimension "hyperspace"? in other words, the 4th space dimension would take the place of time, for a coordinate observer?

In three dimensions physical objects have an extent ( non-zero length ) along all three dimensions. If it is accepted that the four dimensions of general relativity correspond to physical reality, does that imply that physical objects also have a non-zero ( non-infinitesimal ) extent along...

1. Homework Statement Find the dimension of the set of 7x7 matrices with zero trace Relevant Equations The dimension of a standard basis matrix n x n is n^2 Zero trace = sum of diagonal elements = 0 Attempt at Solution I started with dim(M) = n^2 where M is an nxn matrix. Then I...

Homework Statement A football player kicks a field goal from a distance of 45m from the goalpost. The football is launched at 35 degrees above horizontal. What initial velocity is required so that the football just clears the goalpost crossbar that is 3.1m above the ground? ignore air...

How do we know that the (effective) dimensionality of "space" is three in a typical physical theory?

Homework Statement Let V\subset\,R^n be a subpace with dim(V) = D. Prove that any S vectors in V are linearly dependent if S > D. Homework Equations Rank-nullity theorem? The Attempt at a Solution dim(V) = D implies that there are D vectors in a basis for V. If S > D then there...

I just want to clear this up: why can't 5th till 11th dimension be represented in 3 dimensions no matter how small this extra dimensions are? One analogy for an extra dimension is a long rope that represents one dimension but this rope is composed of thinner twisting ropes which now represent...

From what I know, in 2 dimensions gravity works as 1 / R, 3 dimensions is 1 / R^2, and in 4 dimensions 1 / R^3 But what about one dimension? Is it just proportional to R? So the formula would be F = GMMR? Please explain in detail, how gravity would behave in one dimension and how...

I'm familiar with the notion of the dimension of a vector space. Sometime earlier though, I ran into something asking for the dimension of a set of matrices. In general context, what is meant by the dimension of a set?

Hi everyone! I am thinking about, how can calculate the Hausdorff dimension of the Cantor set? I know, that this dimension is \frac{\log 2}{\log 3} but I cannot prove it. Any ideas?

Hi everyone, The problem that I'm having issues with reads: "Let F: Rk →Rn be a linear map. Recall that the graph G(F) of F is the subset of Rk × Rn = Rk+n given by G(F)={(x,y)∈Rk ×Rn : y=F((x)}" It first asked me to show that G(F) is a vector subspace of Rk+n which I did just by the definition...

Homework Statement Given is a vector space (V,+,k) over kn with n > 1. Show that with W \subseteq V, U \subset V and dim(U) = n - 1 dim(W \cap U) \geq dim(W) - 1 Homework Equations dim(W+U) +dim(W \cap U) = dim(W) +dim(V) The Attempt at a Solutiondim(V) = n dim(W) \leq dim(V) dim(W+U)...

Homework Statement I have a question which asks me to find the dimensions of the subspace of even polynomials (i.e. polynomials with even exponents) and odd polynomials. I know that dim of Pn (polynomials with n degrees) is n+1. But how do I find the dimensions of even n odd polynomials...

Let V=Mn(k) be a vector space of matrices with entries in k. For a matrix M denote the trace of M by tr(M). What is the dimension of the subspace of {M\inV: tr(M)=0} I know that I am supposed to use the rank-nullity theorem. However I'm not sure exactly how to use it. I know that the trace is...

Homework Statement Find the basis and dimension of the following subspace U of P2 p(x) \ni P2 such that p(1) = p(2)Homework Equations The Attempt at a Solution I know all quadratics are in the form ax2 + bx + c set p(2) = p(1) 4a + 2b + c = a + b + c b = -3a Therefore ax2 -3a + c Basis(U)...

Homework Statement A car travels north at 30 m/s for one half hour. It then travels south at 40 m/s for 15 minutes. The total distance the car has traveled and its displacement are? Homework Equations The Attempt at a Solution First of all i converted from m/s to km/h. I took...

Hello, please any help will be very much appreciated; A bullet is fired through a board, 14.0 cm thick, with its line of motion perpendicular to the face of the board. If it enters with a speed of 450 m/s and emerges with a speed of 220 m/s, what is the bullet's acceleration as it passes...

Could someone explain the fourth dimension to me? I understand that it represents time. Could anyone thoroughly explain the concept? Thank you.

So a particle of mass M is moving in one dimension given by: x(t) = (alpha)t^2 + (beta)t + (gamma) where alpha, beta, gamma are non zero constants. What are the dimensions of the alpha, beta, gamma? Either the answer is staring right at my face or my physics is rusty :/

dimension of sl(2,R) = 1*(2*2-1) = 3, is isomorphic to so(2,1) : 2+1 = 3 dimension of sl(2,C) = 2*(2*2-1) = 6, is isomorphic to so(3,1) : 3+2+1 = 6 dimension of sl(2,H) = 15, is isomorphic to so(5,1) : 5+4+3+2+1 = 15 dimension of sl(2,O) = 45, is isomorphic to so(9,1) : 9+8+7+6+5+4+3+2+1 = 45...

This should be a simple question for anyone familiar with basic algebraic geometry, but the concept is getting the best of me. Basically I am unclear on the concept of dimension of a variety. I'm still stuck in the algebraic mindset that dimension is the (minimum) number of elements needed to...

Homework Statement In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 79.0 km/h , to his enemy's car, which is going 116 km/h . The enemy's car is 16.1m in front of the hero's when he let's go of the grenade. If the hero throws the grenade so...

I read Stephen Hawking new book and did a little research on M-theory. Apparently in the 11th dimension there are different brains that crash into each other. 2 of these brains crashing supposedly rendered our big bang, and explains why stuff came out in blobs (not homogeneous). But how...