Symmetric Definition and 539 Threads

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 Schrödinger 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...

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...

Homework Statement In Velleman's "How to Prove it", he gives a proof that "R is symmetric iff R = R-1, which I find to be confusing when he is proving that R^{-1}\subseteq{R}: Now suppose (x,y)\in R^{-1}. Then (y,x)\in R, so since R is symmetric, (x,y)\in R. Thus, R^{-1}\subseteq R so R=R-1...

Hi, Is there a simplification for the determinant of a symmetric matrix? For example, I need to find the roots of \det [A(x)] where A(x) = \[ \left( \begin{array}{ccc} f(x) & a_{12}(x) & a_{13}(x) \\ a_{12}(x) & f(x) & a_{23}(x) \\ a_{13}(x) & a_{23}(x) & f(x) \end{array}...

Hi everyone There is a question which I find very hard to solve and it goes like this.. A symmetric coin with heads on one side and tails on the other side is tossed 491 times after one another. The total amount of times you get tails is either even or odd. Is the probability that you get...

Homework Statement My book states as follows: --- If u and v have the coordinate vectors X and Y respectively in a given orthonormal basis, and the symmetric, linear map \Gamma has the matrix A in the same basis, then \Gamma(u) and \Gamma(v) have the coordinates AX and AY, respectively. This...

we can solve non-homogeneous equations in matrix form using Cramer's rule. This rule is valid only if we are replacing the columns. Why can't we replace the rows and carry on the same? For eg we can use elementary transformations for obtaining inverses either via rows or via columns. But we...

Homework Statement Find parametric equations and symmetric equations for the line through P0 and perpendicular to both given vectors. (P0 corresponds to t = 0.) P0 = (1, 1, 0) i + j and j + k Homework Equations The Attempt at a Solution For the symmetric equations, I did...

:confused: friends, we know that fermions must be described by antisymmetric and bosons by symmetric wavefunctions. but i was wondering why a particle of certain class behaves like that for ever? ie. say, an electron will never behave like a boson ?? my book says that there is a spin...

I'm studying the properties of the energy momentum tensor for a scalar field (linked to the electromagnetic field and corresponding energy-momentum tensor) and now I'm facing the statement: "for a theory involving only scalar fields, the energy-momentum tensor is always symmetric". But I've...

Homework Statement Given a real diagonal matrix D, and a real symmetric matrix A, Homework Equations Let C=D*A. The Attempt at a Solution How to prove all the eigenvalues of matrix C are real numbers?

Help! Symmetric matrix I know that all the eigenvalues of a real symmetric matrix are real numbers. Now can anyone help out how to prove that "all the eigenvalues of a row-normalized real symmetric matrix are real numbers"? Thank you~~~

Homework Statement Suppose ~ is defined on the whole numbers by a~b iff ab2 is a perfect cube. Determine if ~ is symmetric transitive Homework Equations ab2 must ba2 The Attempt at a Solution I tried using different numbers, but it isn't coming out as a perfect square. For...

What does "axially symmetric" mean mathematically? If we, for example, say that a magnetic field \vec B is axially symmetric, does that mean that (in cylindrical coordinates) we have \frac{\partial \vec B}{\partial \phi} = 0, where \phi is the azimuthal angle?

Homework Statement Hello, Can you confirm that what I wrote is correct for the given potential? https://www.physicsforums.com/attachment.php?attachmentid=22309&stc=1&d=1260118852 Now I wrote the term for the wave funcation and for the given symetric potential , the functions of the...

Homework Statement Prove a symmetric (2x2) matrix always has real eigenvalues. The problem shows the matrix as {(a,b),(b,d)}. Homework Equations The problem says to use the quadratic formula. The Attempt at a Solution From the determinant I get (a-l)(d-l) - b^2 = 0 which...

symmetric matrices... help please! hi can someone tell me...how to correctly use the 10 axioms.. for example: does the set of all 3x3 symmetric matrices form a subspace of a 3x3 matrices under the normal operations of matrix addition and multiplication? I don't really get how to prove this..

Homework Statement Prove that any square matrix can be written as the sum of a symmetric and a skew-symmetric matrix Homework Equations For symmetric A=A^{T} For scew-symmetric A=-A^{T} The Attempt at a Solution Not sure where to begin. Using algebra didn't work. Got powers...

Hello everyone. This is my first official post here but I have been lurking around for about a year now. Homework Statement Prove that a matrix A is symmetric if and only if x*Ay = Ax*y for all x,y of R^n, where * denotes the dot product. Homework Equations The Attempt at a...

Could some one explain how a bridge rectifier works with a diagram and its mathematics? Also please explain how a center tap transformer and a bridge rectifier are used to provide a symmetric power supply. I have the Ckt Diagram for that but I cannot understand its working. thanks...

Is there a way to prove generally that the Dihedral group and its corresponding Symmetric group of the same order are isormorphic. In class we were only shown a particular example, D3 (or D6 whatever you wish to use) and S3, and a contructed homomorphism, but how could you do it generally? Would...

Homework Statement Show that if A is skew symmetric, then Ak is skew symmetric for any positive odd integer k. Homework Equations The Attempt at a Solution Wow, I have no idea how to prove this. I'm guessing there's going to be induction involved. I know that the base case of k...