Symmetric Definition and 539 Threads

Hi, I'm currently trying to teach myself some measure theory and I'm stuck on trying to show the following: Let (X,M,\mu) be a finite positive measure space such that \mu({x})>0 \forall x \in X . Set d(A,B) = \mu(A \Delta B), A,B \in X. Prove that d(A,B) \leq d(A,C) + d(C,B) . Could...

Hello, my name is Calleigh and i am new to the forum! I am in Calculus II and have a few questions on some problems. I am using the textbook Calculus 8th edition by Larson, Hostetler and Edwards. Could someone please help me? The problem is on pg 950 in chapter 13.7 in the text, number 46. It...

What is the order of S4, the symmetric group on 4 elements? Compute these products in order of S4: [3124] o [3214], [4321] o [3124], [1432] o [1432]. Can I get help on how to do this. The solution's manual gives the answer on how to do the last two, but I don't understand the process...

a weird "spherically symmetric" metric Minkowski metric in spherical polar coordinates [t, r, theta, phi] is ds^2 = - dt^2 + dr^2 + r^2\,(d\theta^2 + sin^2(\theta)\, d\phi^2). The question is what happens when the coefficient of the angular part is set to constant, say 1, instead of r^2...

Determine whether the following digraph represents a relation that is reflexive, symmetric, or transitive. Not sure how to determine this. Any help would be wonderful. The digraph is uploaded into a word document.

So, I was thinking about a variation on the Twin Paradox, and was hoping someone could help me work through it. The motivation is the usual explanation for the Twin Paradox, namely that one twin accelerates and so breaks the symmetry. This begs the question of what happens when both twins ride...

[SOLVED] Center of Symmetric Group Homework Statement Show that for n ≥ 3, Z(Sn) = {e} where e is the identity element/permutation. The attempt at a solution It is obvious that e is in Z(Sn). If there is another element a ≠ e in Z(Sn), then... There must be some sort of contradiction and...

Homework Statement Self-Reproducing Rays in a symmetric Resonator. Consider a symmetric resonator using two concave mirrors of radii R separated by a distance d=3|R|/2. After how many round trips through the resonator will a ray retrace its path? Homework Equations The Attempt at...

X a subset of R^n is called centrally symmetric if the isometry f_z:R^n->R^n defined by x|->2z-x for some z in R^n satisifies: f_z(X)=X. and z is called centre of symmetry. Now i need to show that: 1. if X is centrally symmetric and f is an isometry then f(X) is also centrally symmetric. 2...

Homework Statement Find the coordinates of the symmetric point of the point M(2,1,3) of the line \frac{x+2}{1}=\frac{y+1}{2}=\frac{z-1}{-1} Homework Equations The Attempt at a Solution Out from here: \frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}...

Homework Statement Find the coordinates of the symmetric point of the point M(3,4,7) from the plane 2x-y+z+9=0 Homework EquationsThe Attempt at a Solution I found the equation of the plane which the symmetric point is staying at: 2x-y-z+27=0 Also I found the distance between M(3,4,7) and...

Homework Statement relation A = {a,b,c} for the following matrix [1,0,0;1,1,0;0,1,1] is it reflexive, transitive, symmetric, antisymmetric Homework Equations ordered pairs. The Attempt at a Solution i wrote the ordered pairs as (a,a),(b,a),(b,b),(c,b),(c,c) I only that...

Homework Statement A symmetric building has a roof sloping upward at 34.0 degrees above the horizontal on each side. A)If each side of the uniform roof weighs 1.10×10^4N , find the horizontal force that this roof exerts at the top of the wall, which tends to push out the walls...

A 10.0 gram piece of styrofoam carries a net charge of -0.700\muC and floats above the center of a large horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet? Homework Equations \Phi = E\intdA =...

2. Write a MATLAB® function to calculate the condition number of a symmetric square matrix of any size by means of Eigenvalues: § The power method should be used to calculate the Eigenvalues. § The script (function) should give an error message if the matrix is not...

Homework Statement A = [ b c ... 0000000000000000000 ] [ c b c ... .000000000000000 0] [ ... ] [ 000000000000000000 c b c ] [ 000000000000000000 b c ] where a,b are real. This matrix is tridigonal and symmetric. I need to...

Geometric Algebra for Physicists, in equation (4.56) introduces the following notation A * B = \langle AB \rangle as well as (4.57) the commutator product: A \times B = \frac{1}{2}\left(AB - BA\right) I can see the value defining the commutator product since this selects all...

Homework Statement Solve this equation, and find x. 6x^5-5x^4-29x^2-5x+6=0 Homework Equations if x= \alpha is root of the symmetric equation, then x= \frac{1}{\alpha}, is also root of the symmetric equation The Attempt at a Solution I tried first to write like this...

Homework Statement c) For such a "symmetric" object, prove that any axis going through the center of mass is a principal axis. Homework Equations The Attempt at a Solution I am not sure how they want me to prove this. I was looking at the Displacement Axis Thm but I am not sure...

Find the parametric and symmetric equations of the line of intersection of the planes x+y+z=1 and x+z=0. I got the normal vectors, <1,1,1> and <1,0,1> and their cross product <1,0,-1> or i-k. I set z to 0 and got x=0, y=1, z=0. How do I form parametric equation out of this?? I know...

I heard that one can solve 2D problem with conformal mapping of complex numbers. Is it possible to use this method for 3D axial-rotationally symmetric problems (which are effectively 2D with a new term in the differential equation)?

let B be a nXn real symmetric and non-positive definite matrix. Show that (x^TBx)^1/2 is not a norm on R^n.

Hi, Can anyone help me to understand the following please? If a potential is symmetric does this mean that the eigenstates are either symmetric or antisymmetric? Is the ground state always symmetric and the first excited state always antisymmetric? Thanks!

My dad came across this phrase in a book but neither of us are familiar with it. The statement is : "Let M_{1} and M_{2} be matrices. N = M_{1}^{-1}M_{2}. This matrix is M_{1} symmetric and so it diagonalisable in \mathbb{R}^{2}." Does it just mean that M_{1}=M_{1}^{T} or something else...

For a spherical symmetric potential, the wavefunction can be expanded in terms of partial waves which is dependent on r and \theta . How would this be possible, when the potential only depends on distance from source? Classically, there's no quantity, that could have depend even on \theta .

hi i just wanted a quick explanation of what a symmetric matrix is and what they mean by the quadratic form by the standard basis? (1) for example why is this a symmetric matrix [1 3] [3 2] and what is the quadratic form of the matrix by the standard basis? (2) also how would i go...

1) Let f: V x V -> F be a symmetric bilinear form on V, where F is a field. Suppose B={v1,...,vn} is an orthogonal basis for V This implies f(vi,vj)=0 for all i not=j =>A=diag{a1,...,an} and we say that f is diagonalized. ============ Now I don't understand the red part, i.e. how does...

Homework Statement Let {e1, e2, e3} be a basis for vector space V. Show that the rank 2 tensor g defined by g=2E1*E2 + 2E2*E1+E1*E3+E3*E1 (where Ei are dual vectors and * is the tensor product) is symmetric and nondegenerate. Caculate g inverse. Homework Equations Um. lots of tensor stuff...

Homework Statement If t_{ab} are the components of a symmetric tensor and v_a are the components of a vector, show that if: v_{(a}t_{bc)} = 0 then either the symmetric tensor or the vector = 0. Let me know if you are not familiar with the totally symmetric notation. Homework...

Homework Statement Find an expression for the electrostatic self-energy of an arbitrary spherically symmetric charge density distribution p(r). You may not assume that p(r) represents any point charge, or that it is constant, or that it is piecewise constant, or that it does or does not cut...

Given the vector space consisting of all bilinear forms of a vector space V (let's call it B) it's very easy to prove that B is the direct sum of two subspaces, the subspace of symmetric and the subspace of skew symmetric bilinear forms. How would one go about determining the dimension of these...

Homework Statement The time-independent Schrodinger equation solutions for an infinite well from 0 to a are of the form: \psi_n(x) = \sqrt{2/a} \sin (n \pi x/ a) If you move the well over so it is now from -a/2 to a/2, then you can replace x with x-a/2 and get the new equations right? If I...

Homework Statement Suppose H is an n by n real symmetric matrix. v is a real column n-vector and H^(k+1)v = 0. Prove that Hv = 0 The Attempt at a Solution Since H is a real symmetric matrice we can find an orthogonal matrix Q to diagnolize it: M = Q transpose. MA^(k+1)Qv = 0...

Hi, everyone. I am preparing for a prelim. in Diff. Geometry, and here is a question I have not been able to figure out: I am trying to show that Sym(n) , the set of all symmetric matrices in M_n = all nxn matrices, is a mfld. under inclusion. I see two...

I never learned this in the lectures (maybe I was sleeping), but now I think I finally realized what is the reason that eigenstate solutions of SE with a symmetric potential are either symmetric or antisymmetric. Is the argument this: "The Hamiltonian and the space reflection operator...

Seems to me I was taught in college physics that either a spherical "antenna" could not radiate or an antenna could not radiate spherically. Are either true? How about for an acoustical spherical membrane? For quadrupole mediated gravity?

This isn't really homework, but close enough. I suppose this is quite simple, but my head's all tangled up for today. Anyways, Given the real symmetric matrix LTL = UDUT, find L. I suppose L = +- D1/2UT, and it's clear this choice of L satisfies the given equation. But can it be proven that...

Homework Statement I only just started thinking about this, so I apologize if I can't frame it correctly... But say I have a completely uniform beam sitting on, say, 8 supports all distributed evenly about the beam's center of mass (which is also its geometric center). That is, for every one...

I'm having trouble understanding a certain matrix problem. -Show that AA^T and A^TA are symmetric. -Show that A+A^T is symmetric. Any help would be greatly appreciated.

Is the matrix of a second order symmetric tensor always symmetric (ie. expressed in any coordinate system, and in any basis of the coordinate system)? Please help! :blushing: ~Bee

Hi to our nice community. I want to learn why in a binary symetric channel the channel is calculated as C=1+plogp+(1-p)log(1-p) I only know that the channel is denoted as C=maxI(X;Y) btw what ; means in X;Y? Unfortunately my book doesn't mention these things so if u can reply me or...

Homework Statement Consider a symmetric n x n matrix A with A² = A. Is the linear transformation T(x) = Ax necessarily the orthogonal projection onto a subspace IR^n? Homework Equations The Attempt at a Solution No idea what thought to begin with.

Does anyone know any reference or proof to the statement that since a flow is irrotational, the Jacobian is symmetric?

Homework Statement A particle in a spherically symmetric potential is in a state described by the wavepacked \psi (x,y,z) = C (xy+yz+zx)e^{-alpha r^2} What is the probability that a measurement of the square of the angular mometum yields zero? What is the probability that it yields...

This is a T/F question: all symmetric matrices are diagonalizable. I want to say no, but I do not know how exactly to show that... all I know is that to be diagonalizable, matrix should have enough eigenvectors, but does multiplicity of eigenvalues matter, i.e. can I say that if eignvalue...

How to test if a distribution is symmetric?? Hi all: To test if a distribution is symmetric or not, I knew we can use the mean-median == 0 and skewness == 0 I am wondering if there is any other methods of doing so? Also, which one of them are more...

This is the problem that I am working on. Find a basis for the vector space of all 3x3 symetric matricies. Is this a good place to start 111 110 100 using that upper triangular then spliting it into the set. 100 010 001 000 000 000 000 000 000 100 010 000 000 000 000...

If I have af wavefunction that is a product of many particle wavefunctions $\Psi = \psi_1(r_1)\psi_2(r_2) ... \psi_n(r_n)$ If I then know that the parity of $ \Psi $ is even. Can I then show that the wavefunction i symmetric under switching any two particles with each other. That is...

Homework Statement Let A be a linear operator on a Hilbert space X. Suppose that D(A) = X, and that (Ax, y) = (x, Ay) for all x, y in H. Show that A is bounded. The Attempt at a Solution I've tried to prove it by using the fact that if A is continuous at a point x implies that A is...

"Is it possible to derive the Schwarzschild metric from Killing vectors, thus saving all that work with the Ricci tensor etc."