Symmetric Definition and 566 Threads

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 Show that a closed symmetric operator has a matrix representation. Homework Equations There are lots. I'm hoping somebody familiar with linear operators in Hilbert spaces is reading this! The Attempt at a Solution Hi, I'm trying to prove that a closed...

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...

Can someone give an example of one? I can't think of one...

Homework Statement What am I asked to do in the problem? Am I just asked to draw a diagram or to prove a) and b)? Homework Equations The Attempt at a Solution

The Wikipedia article Metric tensor (general relativity) has the following equation for the metric tensor in an arbitrary chart, g = g_{\mu\nu} \, \mathrm{d}x^\mu \otimes \mathrm{d}x^\nu It then says, "If we define the symmetric tensor product by juxtaposition, we can write the metric in...

Hello, I have a question about a spinning symmetric top: When the equations of motion are solved, they are solved in two frames--the space frame and the body frame. I understand the space frame, but in the body frame you are looking at the top from a frame that is rotating with it, right? So...

spherically symmetric metric used to write in he following form: ds^2 = -h(r,t}^2 * dt^2 + f(r,t)^2 * dr^2 + r^2 * d_omega^2 But what about the form ds^2 = -f(r,t}^2 * dt^2 + f(r,t)^(-1) * dr^2 + r^2 * d_omega^2 and ds^2 = -f(r}^2 * dt^2 + f(r)^(-1) * dr^2 + r^2 * d_omega^2 how...

confusion on "anti-symmetric" and "symmetric" Hi guys, I am a physics sophomore at next term, recently I am doing a reading on Naive Set Theory on my own. However, I got a few confusion. The books said that if A is a subset of B and B is a subset of A, then A=B, but this set inclusion is...

Homework Statement Hello, I need some help in the fist parts of two lineal algebra problems, specially with algebraic manipulation. I guess that if I rewrite the determinant nicely some terms get canceled and I can write the inverse nicely, but don't know how to do it... Problem 1...

Hi, all, According to my script, a connection \nabla_v is symmetric if the following holds (I assume for every pair of vectors): \nabla_v w - \nabla_w v =[v,w] What is the idea behind that? Why are we interested in that kind of symmetry (not for instance 0 instead of the commutator)...

Is a symmetric Lagrangian leads to a symmetric Stress-Energy Momentum ？

Hi, We know that if u is a real symetric endomorphism, then u has a real eigenvalue and that u is diagonalizable. But can we say that u is diagonalizable with only real eigenvalues?

Hello, I guess this is a basic question. Let´s say that If I am given a matrix X it is possible to form a symmetric matrix by computing X+X^{T} . But how can I form a matrix which is both symmetric and orthogonal? That is: M=M^{T}=M^{-1}.

Is there a shorter way to verify this identity, as you can see I haven't even finished it. I know you can use Ven diagrams and truth tables but I wanted to avoid them inorder to use a more general formal approach. picture is attached

okay so i have looked up things online and they when other ppl explain it it still doesn't make sense. I am working on a few specific problems. R = {(2,1),(3,1),(3,2),(4,1),(4,2),(4,3)} the book says this is antisysmetric by sayingthat this relation has no pair of elements a and b with a...

Hi. Let A = 1,2,3,4,5,6,7 How many symmetric relations on A contain exactly (a) four ordered pairs, (b) 5 , (c) seven and (d) eight The book has solutions to the first two, which I didn't understand at all. Please look the pic below Can someone guide me through how to approach the problem...

Is there anyway to show that for a symmetric or normal matrix A, that det(A) = \prod \lambda_i without using Jordan blocks? I want to show this result using maybe unitary equivalence and other similar matrices... any ideas? It's obviously easy with JCF...

Homework Statement The question is, "How many conjugates does (1,2,3,4) have in S7? Another similar one -- how many does (1,2,3) have in S5? The Attempt at a Solution I know that the conjugates are all the elements with the same cycle structure, so for (123) I found there are 20...

Just a quick theory question. I'd assume it is, but usually the bigger number goes first. e.g. gcd(10, 5) = 2 but does gcd (5, 10) = 2? My guess is yes. Thanks for the help.

I need to prove the following. 1. A is a symmetric matrix, and x(transpose)*A*x=0 for all x (belongs to R^n) if and only if A=0. 2. x(transpose)*A*x=0 for all x (belongs to R^n), if and only if A is skew symmetric.

I've been learning GR in my sparetime, and occationally I run into a conceptual problem that stalls my progress. Here is a question that has come up. I expect that this is a stupid question, but it's really bugging me, and an explanation will help me move forward more efficiently. If we wish...

Homework Statement Why is the ground state always symmetric and first excited state anti-symmetric? OR Why does the ground state always have no node and first excited state has one node? Homework Equations The Attempt at a Solution

Electric charge continuity is expressed as ∂tρ + ∂iJi =0. (1) The manifold, M in question is 3 dimensional and t is a parameter, time. ∂iJi is the inner product of the ∂ operator and J. With M a subspace of a 4 dimensional manifold with metric signature -+++, eq. (1) can be written in...

]This isn't a home work question in particular, but just want confirmation about a general idea. So in Calc III, you have integrals of the form \int_{-a}^a \int_{-\sqrt{a^2 - x^2}}^{\sqrt{a^2 - x^2}} x y dy dxwhich is the typical rectangular coordinates for a circle. Now, the integrand is the...

Homework Statement For sets A and B, define a relation \mathcal{R} on A∪B by: \forall A, B \in A \cup B, x\mathcal{R}y if and only if (x,y) \in A \times B For all sets A and B, if R is symmetric, then A = BHomework Equations The Attempt at a Solution I tried doing this, and I heard it's...

When solving the time-independent Schrodinger equation for a spherically symmetric potential, using the separation of variables, we find that solutions of the form \psi =R(r)Y_l^m(\theta ,\phi) where the Y_l^m are the spherical harmonics. We apply this to the (idealized) electron in a Hydrogen...

Does anyone know if it possible to generate elementary symmetric polynomials in Maple (I am using version 12), and if so, how? I have scoured all the help files, and indeed the whole internet, but the only thing I have found is a reference to a command "symmpoly", which was apparently...

Hi everyone, This is related to my previous https://www.physicsforums.com/showthread.php?t=392069" Let A=(a_{ij}) be a symmetric (i.e., over reals) PSD matrix with the following conditions on Leading Principle Minors (determinant of the submatrix consisting of first i rows and i...

Hi everyone, Let A=(a_{ij}) be a symmetric (i.e., over reals) PSD matrix. Then is the following correct? "If any principle minor ( \ne A ) be zero, then all principle minor contained in this minor should also be zero". I can not prove or disprove it..any help? By the way how...

Let f, g \in \mathbb{Z}[x, y, z] be given as follows: f = x^8 + y^8 + z^6 and g = x^3 +y^3 + z^3. Express if possible f and g as a polynomial in elementary symmetric polynomials in x, y, z. Professor claims there is an algorithm we were supposed to know for this question on the midterm. I...

Dear all, I'm trying to solve the 2d heat equation in a radially symmetric domain, numerically using the Crank-Nicolson method. i.e. \dfrac{\partial u}{\partial t} = D\left( \dfrac{\partial^2u}{\partial r^2}+\dfrac{1}{r}\dfrac{\partial u}{\partial r}\right) Applying the Crank-Nicolson...

I would like to ask you what it is meant by "symmetric input" in the instrumentational amplifier schematics and in the differential amplifier? I can`t understand what is the difference between symmetric and non symmetric input and output as parameters. Can anyone explain ? Thanks

Homework Statement 5.1: Prove that S_n is generated by the set {(1 2), (3 4),...,(n-1 n)}Homework Equations None that I know ofThe Attempt at a Solution Any element in S_n can be written as a product of disjoint n-cycles. So now I need to show any n-cycle can be written as a product of...