Symmetric Definition and 539 Threads

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110804_134032.jpg?t=1312484230 http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110804_134038.jpg?t=1312484242 I found that the order of G/H is 6. According to the Lagrange's Thereom, order of G = order of H *...

Hi there, I'm trying to figure out proving the following: if X oplus Y = Y oplus X then X = Y In order to prove it, I need to use the symmetric difference associativity & other characteristics and identities. Can you please give me a direction? Please explain the answer as a teacher...

I'm reading from Wikipedia: I thought linear operators always had eigenvalues, since you could always form a characteristic equation for the corresponding matrix and solve it? Is that not the case? Are there linear operators that don't have eigenvalues?

Homework Statement There is a symmetric difference in sets X & Y, X Y is defined to be the sets of elements that are either X or Y but not both Prove that for any sets X,Y & Z that (X\oplusY)\oplus(Y\oplusZ) = X\oplusZ Homework Equations \oplus = symmetic difference The Attempt at...

Why are the Time Symmetric Interpretation rarely if ever brought up in discussions here? It restores determinism and realism. This article explains the jist of the interpretation and experimental evidence...

Express \left(\begin{array}{cccc} 6 & 1 & 5\\ -2 & -5 & 4\\ -3 & 3 & -1\ end{array} \right) as the sum of the symmetric and skew symmetric matrices. I did this following way Consider symmetric metric as "A" then; A = \left(\begin{array}{cccc} 6 & 1 & 5\\ 1 & -5 & 4\\ 5 & 4 & -1\ \end{array}...

Hi all, I have a set of equations that look very nice and symmetric, but the only way I'm able to find solutions to them is with pages and pages of algebra! Can any members with more of a mathematical flair than myself point me in the direction of a more direct and satisfactory method of...

Homework Statement For n>1, show that the subgroup H of S_n (the symmetric group on n-letters) consisting of permutations that fix 1 is isomorphic to S_{n-1} . Prove that there are no proper subgroups of S_n that properly contain H.The Attempt at a Solution The first part is fairly...

Homework Statement Use induction of n to prove that the transpositions s_i = (i, i+1), 1 \leq i \leq n - 1 generate S_n. Homework Equations Notation: e = Identity permutation. Any permutation can be written as a disjoint product of transpositions. The Attempt at a Solution...

Hi, I'm trying to determine the exact transformation that brings a spherically symmetric spacetime metric in spherical coordinates to the Sylvester normal form (that is, with just 1 or -1 on its main diagonal, with all other elements equal to zero.) Assuming that the metric has Lorentzian...

According to duality principle, a bilinear function \theta:V\times V \rightarrow R is equivalent to a linear mapping from V to its dual space V*, which can in turn be represented as a matrix T such that T(i,j)=\theta(\alpha_i,\alpha_j). And this matrix T is diagonalizable, i.e...

Is it possible that whatever cause the big bang to happen and make space expand also (for lack of a better phrase) tore time in two? Resulting in two universes moving in opposite directions of time, and could this be used to explain why there appears to be more matter then antimatter in the...

I have read in a couple of places that mixed tensors cannot be decomposed into a sum of symmetric and antisymmetric parts. This doesn't make any sense to me because I thought a mixed (1,1) tensor was basically equivalent to a standard linear transform from basic linear algebra. I am also...

Homework Statement No problem exactly I am just reading a book that refrences symmetric polynomials but i don't know what a symmetric polynomial is. I looked at the wiki page but i didn't really get what it was saying. Any help on clearing up the meaning would be greatly appreciated...

As is well known, a Dirac Lagrangian can be written in a symmetric form: L = i/2 (\bar\psi \gamma \partial (\psi) - \partial (\bar\psi) \gamma \psi ) - m \bar\psi \psi Let \psi and \psi^\dagger be independent fields. The corresponding canonical momenta are p = i/2 \psi^\dagger...

It is a well known fact that a symmetric bilinear form B on a finite-dimensional vector space V over any field F of characteristic not 2 is diagonalisable, i.e. there exists a basis \{e_i\} such that B(e_i,e_j)=0 for i\neq j. Does the same hold over an infinite dimensional vector space...

thanks

Is every complex symmetric (NOT unitary) matrix M diagonalizable in the form U^T M U, where U is a unitary matrix? Why?

Hi, How does one define symmetry of a system? I believe that a scalar function g(\vec x) is called symmetric under a transformation \vec F(\vec x) if and only if g(\vec x) = g(\vec F(\vec x)) If there is an equivalent criteria for vector functions, I would be inclined to define a...

Homework Statement The bilinear form are symmetric, i.e. a(u,v) = a(v,u) for all u and v. Find the bilinear form and the linear functional for the problem -\Deltau + b . \nablau + cu = f(x) in \Omega u = 0 on the boundary. Is this bilinear form for this problem symmteric? Is it coersive...

how can we prove that the rank of skew symmetric matrix is even i could prove it by induction is there another way

Hi, I am working with a Galerkin FEM implementation of an elastodynamic problem in the frequency domain. For the purely elastic case, this results in a symmetric, positive definite linear system that is efficiently solved by Cholesky decomposition. In order to consider anelasticity, however...

I'm just trying to get a feel for how seriously this theory is being considered these days. For those not familar with it, here's a somewhat okay laymans description: http://discovermagazine.com/2010/apr/01-back-from-the-future/article_view?searchterm=Tollaksen&b_start:int=0 Also...

Homework Statement Hello, I want to make sure that I graphed the directed graphs in my homework correctly. The problems and my work is located in the attachment. I also uploaded the directed graphs onto this link: http://img857.imageshack.us/f/83289329.png/" Homework Equations NoneThe Attempt...

Homework Statement What conclusion can be drawn from the lines (x-x0)/a = (y-y0)/b = (z-z0)/c (x-x0)/A = (y-y0)/B = (z-z0)/C if aA + bB +cC = 0 Homework Equations The Attempt at a Solution I put everything in parametric form but that didn't do much for me. Is...

a)Find a basis for the space of 2x2 symmetric matrices. Prove that your answer is indeed a basis. b)Find the dimension of the space of n x n symmetric matrices. Justify your answer.

Homework Statement Show that if G is a subgroup of a symmetric group Sn, then either every element of G is an even permutation or else exactly half the elements of G are even permutations. Homework Equations The Attempt at a Solution We have a hint for the problem. If all the...

Homework Statement Let L(x) a linear operator defined by setting the diagonal elements of x to zero. What will be the representation of this operator to the following basis set? x E X. X denote the set of all real symmetric 3x3 matrices. Homework Equations L*y=x L=x*inv(y)...

Why must we have g_{\mu\nu}=g_{\nu\mu}? What are the physical consequences if this did not hold?

Hi all, I'd like to define a vector valued function in mathematica 7 as the exponential of a quadratic form, defined with respect to a purely symbolic matrix. What I want to do with it is to take derivatives with respect to the components of my vector, and evaluate the result when all...

I'm pretty inexperienced in proof writing. So not sure if this was valid. If a matrix is skew symmetric then A^T = - A, that is the transpose of A is equal to negative A. This implies that if A = a(i,j), then a(j,i) = -a(i,j). If we're referring to diagonal entries, we can say a(j,j) =...

Homework Statement Let W be a 3x3 matrix where A^t(transpose)=-A. Find a basis for W. Homework Equations Find a basis for W. The Attempt at a Solution I have no idea how to start it.

I am a bit confused by this observation. Every tensor is it's symmetric plus antisymmetric part. Thus for the components of a (0,3) tensor F_{\lambda\mu\nu}=F_{[\lambda\mu\nu]}+F_{\{\lambda\mu\nu\}} and if I write this down explicitly I end up that for the components of ANY (0,3)...

Homework Statement Imagine a spherically symmetric charge density p(x) = Cr for r≤a and 0 for r>a (a) determine the electric field E(x) and potential V(r). Notice that V(r) and E(x) are continuous at r=a. (b) Now suppose additional charge is placed uniformly on the surface at r=a, with...

How can I explain that the fact that a covariant second rank tensor is symmetric in one coordinate system is a tensorial property. This is for my GR course, but I didn't do a Tensor Calculus before.

Can anyone prove that the eigenvectors of symmetric matrices are orthogonal?

Can a symmetric matrix contain complex elements(terms). If no, how is it that 'eigen values of a symmetric matrix are always real'(from a theorem) Is a symmetric matrix containing complex terms called a hermitian matrix or is there any difference? Can we call the following matrix...

Can someone explain to me how to show (x\y) union (y\x) = (x union y) \ (y union x) using only the main set theory laws for union, intersections and difference.

Homework Statement If A is a symmetric matrix, what can you say about the definiteness of A^2? Explain. Homework Equations I believe I need to use the face that A^2=SD^2S^-1. I know that if all the eigenvalues of a symmetric matrix are positive then the matrix is positive...

Homework Statement S : T = S:[0.5(T+TT)] S is a symetric tensor show for any tensor T the above is valid Homework Equations The Attempt at a Solution what i think i know ST=S S:T=tr[STT] =tr[ST] einstein notation tr[SijTjk] [SijTjk]ii but i can't really see this leading to...

Hi Let us suppose we transmit the binary digit '1'. The probability of not receiving '1' is p. Thus the probability of receiving '1' is 1-p. Suppose we send a longer code of length n. The probability of this code being received correctly is (1-p)^n. Now I don't understand this next...

Homework Statement f: [-a,a] >. R is Riemann integrable, prove that ∫[-a, a] ƒ (x) dx = 0 Homework Equations The Attempt at a Solution This only proof below I can think of is rather very calculus-ish.I wonder is there any other proof that is more Real Analysis level for this problem? Thanks...

Homework Statement what is the Q value for the symmetric fission of 236U? Homework Equations M(Z,A)=Zmp+Nmn-B The Attempt at a Solution I don't understand the question by saying symmetric fission, is it mean we have the reaction which is 236U=118Ru+118Ru so the Q from he...

Homework Statement Prove that S_n and D_n for n>=3 are non-cyclic and non-abelian. Homework Equations I get that I need to show that two elements from each group do not commute and that there is not a single generator to produce the groups... I am just unsure of how to do this...

Homework Statement The question is to show that the for symmetric groups, Sn with n>=3, the only permutation that is commutative is the identity permutation. Homework Equations I didn't know if it was necessary but this equates to saying the center is the trivial group. The Attempt at...

Is General Relativity Time Symmetric?

I am really confused and the question can appear to be trivial or stupid: Is the Ricci tensor symmetric or anti-symmetric in a torsion-free affine connection? I am full of troubles since two different references gives two different answers (sorry no one is in english language but one of...

Homework Statement The set A has 5 elements. 1. How many relations exist on A? 2. How many of those relations are symmetric and reflexive? The Attempt at a Solution Some of the parts of this question are harder than others. 1. By simple counting, there are 2^(5^2) or 2^25 total relations...

Here is my problem. Any ideas are appreciated. Let P be a projection matrix (symmetric, idempotent, positive semidefinite with 0 or 1 eigenvalues). For example, P = X*inv(X'*X)*X' where X is a regressor matrix in a least square problem. Let A be a symmetric real matrix with only integer...

Hi, I have been at this single problem for two hours with nothing to show for it. Find symmetric equations for the line of intersection of the planes. z = 3x - y - 7 z = 4x + 2y - 6 They also give me one of the symmetric equations, z/10. I have over 3 pages of work for this. I...