Symmetric Definition and 539 Threads

Homework Statement Hi, An equation of the form Ax + By + C = 0 is a standard equation of a line in 2D. An equation of the form Ax + By + Cz + D = 0 is an equation of a plane. Is it possible to: Describe a plane in space, written in standard form, such that one variable is missing from the...

Hi, I need help in proving the following statement: An abelian,transitive subgroup of the symmetric group Sn is cyclic,generated by an n-cycle. Thank's in advance

I was solving this problem and I didn't want to do it the really long way by finding the equation of B(t) by first finding T(t) and N(t). So i took the cross product of r' and r'' so that they would be in the direction of B. Found the parametric equation of the plane but the book answer was in...

Hello all, I have 3 matrices, A - symmetric, B - anti symmetric, and P - any matrix All matrices are of order nXn and are not the 0 matrix I need to tell if the following matrices are symmetric or anti symmetric: 1) 5AB-5BA 2) 4B^3 3) A(P^t)(A^t) 4) (A+B)^2 5) BAB How would you approach...

Homework Statement I try to run this program, but there are still some errors, please help me to solve this problems Homework EquationsThe Attempt at a Solution Program Main !==================================================================== ! eigenvalues and eigenvectors of a real...

Homework Statement I am looking for some quick methods to integrate while leaving each step in its vector form without drilling down into component-wise integration, and I am wondering whether it is possible here. Suppose I have a square domain over which I am integrating two functions w and...

Homework Statement Let A=RxR=the set of all ordered pairs (x,y), where x and y are real numbers. Define relation P on A as follows: For all (x,y) and (z,w) in A, (x,y)P(z,w) iff x-y=z-w Homework Equations R is reflexive if, and only if, for all x ∈ A,x R x. R is symmetric if, and only if, for...

In special relativity a sphere in the rest frame for some observer looks like an ellipsoid for an observer with a relative velocity. Can we use the same reasoning for the Schwarzschild spacetime? Namely that a spherically symmetric spacetime produced by a spherical mass look ellipsoidal for an...

Suppose that R1={(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}, R2={(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}, R3={(2,4),(4,2)} , R4={(1,2),(2,3),(3,4)}, R5={(1,1),(2,2),(3,3),(4,4)}, R6={(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)}, Determine which of these statements are correct. Check ALL correct answers...

Can anyone explain or point me to a good resource to understand these operators? I'm trying to the understand determinants for skew symmetric matrices, more specifically the Moore determinant and it's polarization of mixed determinants. Can hone shed some light? I'm confused as to how the...

Hello fellow engineers! I am a student doing a simple course in Electrical Engineering. I've got an enquiry regarding this question " 1. In a three phase 4 wire system with phase to neutral voltage of 230V, a balanced set of resistive loads of 8 ohms are connected between each phase and...

Can some one write for me the Symmetric part of a third order tensor (as a tensor form) Thanks .

A maximally symmetric is a Riemannian n-dimensional manifold for which there is n/2 (n+1) linearly independent (as solutions) killing vectors. It is well known that in such a space $$R_{abcd} \propto (g_{ab}g_{cd} - g_{ac}g_{bd}) .$$ How is this formula derived for a general maximally...

Homework Statement Imagine a spherically symmetric charge density p(r)=Cr for r<=a, p(r)=0 for r>a. a) Find the electric field E(r) and potential V(r). Are they continuous at r=a? b) Suppose additional charge is placed uniformly on the surface at r=a with surface density sigma. Find E(r) and...

I have been looking on the web but I can't seem to find a textbook answer that describes the difference between microfluidic t-junctions that are symmetric and those that are asymmetric. From some papers I've gathered that you can make t-junctions asymmetric by changing the hydraulic resistance...

I have been looking on the web but I can't seem to find a textbook answer that describes the difference between microfluidic t-junctions that are symmetric and those that are asymmetric. From some papers I've gathered that you can make t-junctions asymmetric by changing the hydraulic...

Hello everyone, as I know the regular precession of torque-free symmetric top is such a cliche, I'll try to keep derivations short. The goal is, as I pointed out, to inspect a behaviour of the torque-free symmetric top in terms of precession rate, rotation rate and nutation angle. One way is to...

[SIZE="4"]Definition/Summary The symmetric group S(n) or Sym(n) is the group of all possible permutations of n symbols. It has order n!. It has an index-2 subgroup, the alternating group A(n) or Alt(n), the group of all possible even permutations of n symbols. That group has order n!/2...

Please could someone explain to me what is meant by the radially symmetric "breathing resonance" of a sealed water filled tube or cell? That is with the use of transducers this can be achieved, but what does it mean? is it talking about generating a standing wave in the fluid? It relates...

Hello, In CFD computation of the Navier-Stokes Equation, is stress tensor assumed to be symmetric? We know that in NS equation only linear momentum is considered, and the general form of NS equation does not assume that stress tensor is symmetric. Physically, if the tensor is asymmetric then...

Hi, While studying Lie groups and in particular the representations I have some trouble with determining whether a representation is a symmetric, antisymmetric or mixed tensor product of the fundamental representations. I'm working with SO(5) to get an understanding about the actual...

It seems that the only applicable use I've seen is in finding intercepts on various axes. Are there any other instances where this form would used? What else can this be used for?

I am trying to understand this apparent "paradoxes" but probably i am missing something important. Imagine that accourding to stationary observer on Earth two twin cats are moving in the opposite directions with speed -v and v. When the two cats meet the stationary observer at the beginning O...

Homework Statement From Mary Boas' "Mathematical Methods in the Physical Science" 3rd Edition Chapter 3 Sec 11 Problem 33 ( 3.11.33 ). Find the eigenvalues and the eigenvectors of the real symmetric matrix. $$M=\begin{pmatrix} A & H \\ H & B \end{pmatrix}$$ Show the eigenvalues are real and...

Hello, What is the most general cylindrically symmetric line element in the canonical form? Best regards.

Homework Statement Derive Euler's equation of motion for a rigid body: $$\dot{\vec{L}} + \vec{\omega} \times \vec{L} = \vec{G},$$ where ##\vec{L}## is the angular momentum in the body frame, ##\omega## is the instantaneous velocity of the body's rotation and ##\vec{G}## is the external torque...

I am a bit dense when it comes to linear algebra for some reason. I am reviewing math to prepare for a physics grad program, and I am using Mary Boas "Mathematical Methods in the Physical Sciences". She presents the idea of a skew symmetric matrix in the problem set rather than in the text. I...

Homework Statement Consider the following permutation representations of three elements in ##S_3##: $$\Gamma((1,2)) = \begin{pmatrix} 0&1&0\\1&0&0\\0&0&1 \end{pmatrix}\,\,\,\,;\Gamma((1,3)) = \begin{pmatrix} 0&0&1\\0&1&0\\1&0&0 \end{pmatrix}\,\,\,\,\,; \Gamma((1,3,2)) = \begin{pmatrix}...

Hello everyone, I have the functions y_1 = \frac{c}{b} + d e^{-bx} andy_2 = \frac{c}{b} - d e^{-bx} , where c \in \mathbb{R}, and b,d \in \mathbb{R}^+. What I would like to know is how to show that these two functions are symmetric about the line y = \frac{c}{d}. What I thought was that if y_1...

Homework Statement So, we can presumably write that m = g L, where L is the angular momentum, g the ratio wanted, and m magnetic dipole moment of an axially symmetric body. Total mass is M, total charge Q, mass density \rho_m(r)=\frac{M}{Q}\rho_e(r), where \rho_e(r) is charge density...

If we use the "flux of 4-momentum" definition of the stress-energy tensor, it's not clear to me why it should be symmetric. Ie, why should ##T^{01}## (the flux of energy in the x-direction) be equal to ##T^{10}## (the flux of the x-component of momentum in the time direction)?

I asked this question here, however the title of the thread (and the thread itself) was sloppy and unclear.I could not find a way to delete or edit. This is for a regression analysis course, and I've only taken one introductory course on linear algebra, so when I Google'd "finding a symmetric...

Under which conditions is a real positive definite matrix symmetric? I have crossposted here: http://math.stackexchange.com/questions/661102/positive-definite-matrix-symmetric

Homework Statement Show that if a set has 3 elements, then we can find 8 relations on A that all have the same symmetric closure. Homework Equations Symmetric closure ##R^* = R \cup R^{-1} ## The Attempt at a Solution If the symmetric closures of n relations are the same then...

What is minimum possible rank of skew symmetric matrix ?

Hello MHB. During my Mechanics of Solids course in my Mechanical Engineering curriculum I came across a certain fact about $3\times 3$ matrices. It said that any symmetric $3\times 3$ matrix $A$ (with real entries) whose trace is zero is orthogonally similar to a matrix $B$ which has only...

Homework Statement We have a finite group ##G## and a homomorphism ##\rho: G \rightarrow \mathbb{GL}_n(\mathbb{R})## where ##n## is a positve integer. I need to show that there's an ##n\times n## positive definite symmetric matrix that satisfies ##\rho(g)^tA\rho(g)=A## for all ##g \in G##...

Hi everyone, :) Here's a question I am stuck on. Hope you can provide some hints. :) Problem: Let \(U\) be a 4-dimensional subspace in the space of \(3\times 3\) matrices. Show that \(U\) contains a symmetric matrix.

Can one say that every general curved spacetime, locally is maximally symmetric? I know that one can say that every general curved spacetime is locally flat (and therefore maximally symmetric with R=0), but I'm talking about a very high curvature spacetime, where still we can consider nonzero...

I've been seeing more and more papers that seem to suggest Time Symmetric Quantum Mechanics (TSQM) is becoming the more parsimonious explanation to some newer experiments. For those unfamiliar with this formulation, it's a two-state-vector formulation, with one of the state vectors...

When I start to read the the article called "symmetric bi-linear forms", I face the following sentence. But I don't understand what does the following sentence suggest. Could someone please help me here? We will now assume that the characteristic of our field is not 2 (so 1 + 1 is not = to 0)

Hello fellow physicists, I have a query about a practical matter. I'm trying to simulate the rotational spectrum of a symmetric top and so far I've been able to produce a stick spectrum of it. My first problem is that the lines do not exactly match the positions of the peaks but my biggest...

Homework Statement Show that a static, spherically symmetric Maxwell tensor has a vanishing magnetic field. Homework Equations Consider a static, spherically-symmetric metric g_{ab}. There are four Killing vector fields: a timelike \xi^{a} satisfying \xi_{[a}\nabla_{b}\xi_{c]} = 0 and...

Homework Statement In a symmetric positive definite matrix, why does max{|aij|}=max{|aii|} Homework Equations |aij|≤(aii+ajj)/2 The Attempt at a Solution max{|aij|}≤max{(aii+ajj)/2 max{|aij|}≤max{aii/2}+max{ajj/2} max{|aij|}≤\frac{1}{2}max{aii}+\frac{1}{2}max{ajj} then I...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Why are centre of mass of all uniform symmetric bodies at there geometric centre? We know the following result: "Consider a system of point masses m1,m2,m3... located at co-ordinates (x1,y1,z1), (x2,y2,z2)...respectively. The centre of mass of this system of masses is a point whose co-ordinates...

Hi all! I was wondering if \partial_1\partial_2f=\partial_2\partial_1f in a Riemannian manifold (Schwartz's - or Clairaut's - theorem). Example: consider a metric given by the line element ds^2=-dt^2+\ell_1^2dx^2+\ell_2^2dy^2+\ell_3^2dz^2 can we assume that...

Is there an exact solution for the spherical symmetric collaps of pressureless dust? Can one see a Schwarzschild solution for r > Rdust with shrinking Rdust(t) ?

Homework Statement I need to find the normalization constant N_{S} of a symmetric wavefunction ψ(x_{1},x_{2}) = N_{S}[ψ_{a}(x_{1})ψ_{b}(x_{2}) + ψ_{a}(x_{2})ψ_{b}(x_{1})] assuming that the normalization of the individual wavefunctions ψ_{a}(x_{1})ψ_{b}(x_{2}), ψ_{a}(x_{2})ψ_{b}(x_{1}) are...

I am having problems showing the following: ##f## and ##g## are two linearly independent functions in ##E## and ##\theta : \mathbb{R} \to \mathbb{R}## is an additive map such that ##\theta(\mu \nu) = \theta(\mu)\nu +\mu \theta(\nu); \mu,\nu \in \mathbb{R}##. Show that the function; ##\psi...