Symmetric Definition and 539 Threads

I have a system that ideally creates a real symmetric negative definite matrix. However, due to the implementation of the algorithm and/or finite-precision of floating point, the matrix comes out indefinite. For example, in a 2700 square matrix, four eigenvalues are positive, the rest are...

Hi all! I was working on some homework for the linear algebra section of my "Math Methods for Physicists" class and was studying skew symmetric matrices. There was a proof I saw on Wikipedia that proves that the determinant of a skew symmetric matrix is zero if the number of rows is an odd...

what are half wave symmetric waves ? hello friends...i m studying signal n system...i havnt find suitable info about half wave symmetric waves from anywhere...i need to understand that how to find whether any wave is half wave symmetric or not...please help me friends ...

Homework Statement Give the basis and dimension of the set of all 2x2 complex symmetric matrices. Homework Equations The Attempt at a Solution I know that if the coefficients were real, then I could just have the basis \left( \begin{array}{cc} 1 & 0\\ 0 & 0 \end{array}...

Homework Statement Show that \epsilon_{ijk}a_{ij} = 0 for all k if and only if a_{ij} is symmetric.Homework Equations The Attempt at a Solution The first bit I think is just like the proof that a symmetric tensor multiplied by an antisymmetric tensor is always equal to zero. \epsilon_{ijk} = -...

This problem is a symmetric delta potential problem that I was given a few days ago and I can't seem to get the gist of it. Question: Find the spectrum and wave functions of a particle in the potential V(x)=G[d(x-a)+d(x-a)] Calculate the transmission and reflection amplitude. Where G can be...

Hi all, Quick question I haven't been able to find the answer to anywhere: Can I use exterior calculus for symmetric tensors? I'm familiar with the exterior calculus approach to things like Stokes's theorem and Gauss's law, but that's vector stuff. It seems to me the only tensors in...

Problem: Applied Partial Differential Equations (Richard Heberman) 4ed. #12.3.6 Consider the three dimensional wave equation \partial^{2}u/\partial t^2 = c^2\nabla^2 u Assume the solution is spherically symetric, so that \nabla^2 u =...

Hi, I would like to ask a question about spherically symmetric charged objects. My teacher told me that you can treat spherically symmetric charged objects at point charges. However, my teacher did not prove it. I guess you have to integrate every small volume on the spherically symmetric...

1. See Attachments 2. None 3. 1st Attachment #19 I believe that I am suppose to multiply (x-2)(x+2) but what do i do about the symmetric with an origin? 2nd Attachment I do not get what they are asking for in the 2nd and 3rd part of the question can you please explain it to me...

Homework Statement A particle that moves in three dimensions is trapped in a deep spherically symmetric potential V(r): V(r)=0 at r<r_0 infinity at r>= r_0 where r_0 is a positive constant. The ground state wave function is spherically symmetric , so the radial wave function u(r)...

Consider the heat equation in a radially symmetric sphere of radius unity: u_t = u_{rr}+{2 \over r}u_r \ for \ (r,t) \in (0,1) x (0,\infty) with boundary conditions \lim_{r \rightarrow 0}u(r,t) < \infty ; \ u(1,t)=0\ for \ t >0 Now, using separation of variables u=R(r)T(t) leads to the...

Can someone confirm this? If so, are there any respected websites on the net that can confirm this theorem?

I had this question on a test and I was wondering why it is false: If the row space equals teh column space then AT=A.

parametric and symmetric equations in R^3?? Homework Statement Recall that there are three coordinates planes in 3-space. A line in R3 is parallel to xy-plane, but not to any of the axes. Explain what this tells you about parametric and symmetric equations in R3. Support your answer using...

Hello I recall, I think, that there is a lemma which states that a 2x2 symmetric matrix can be diagonalized so that its eigenvalues are (trace) and 0. I can not find it anywhere =/ I think it was a physics teacher who told us this a couple of years ago, can anyone enlighten me? cheers

Guys does anyone know of a technique to find the exponential of a tridiagonal symmetric matrix... Thanks in advance

when a space (or spacetime) is said to be maximally symmetric, does this mean that it is homogeneous?

Homework Statement Find a set of generators for a p-Sylow subgroup K of Sp2 . Find the order of K and determine whether it is normal in Sp2 and if it is abelian. Homework Equations The Attempt at a Solution So far I have that the order of Sp2 is p2!. So p2 is the highest power of...

Homework Statement I am trying solve the 3-D Schrodinger equation for a particle in a cylindrically symmetric potential. If it was the case of spherically symmetric potential, then we can approximate it to a central potential. But what will be the form of the potential in the cylindrically...

Homework Statement Is this relation symmetric? The relation in a set of people, "is brother of" Homework Equations aRb , bRa The Attempt at a Solution The answer is not symmetric. They gave example says that paul may be the bother of Anne but Anne is not the brother of paul...

Is there a difference between Twin grain boundary and symmetric tilt grain boundary? If so, what is it?

Homework Statement Let {u1, u2,...,un} be an orthonormal basis for Rn and let A be a linear combination of the rank 1 matrices u1u1T, u2u2T,...,ununT. If A = c1u1u1T + c2u2u2T + ... + cnununT show that A is a symmetric matrix with eigenvalues c1, c2,..., cn and that ui is an eigenvector...

Homework Statement How to find such a presentation? Where would one start?

Homework Statement consider the 2*2 symmetric matrix A = (a b ) (b c) and define f: R^2--R by f(x)=X*AX . show that \nablaf(x)=2AX Homework Equations The Attempt at a Solution quiet confuse about this question \nablaf(x)=(Homework Statement consider the 2*2 symmetric matrix A...

Hi all, I'm wondering if the following argument is right: "The optimum (minimum/maximum) value of a symmetric function f(x_1,x_2,...,x_n) (By 'symmetric' I mean that f remains same if we alter any x_i's with x_j's), if exists, should be at the point x_1=x_2=...=x_n". Please help me by...

Prove: the set of 3x3 symmetric matrices is a vector space and find its dimension. Well in class my prof has done this question, but I still don't quite get it.. Ok, first off, I need to prove that it's a vector space. The easy way is probably to prove that it contains the zero space and...

A symmetric operator has a maximal symmetric extension. How do you prove this?

Homework Statement Let A be a real symmetric positive definite matrix. Show that |aij|<(aii+ajj)/2 for i not equal to j. Homework Equations The Attempt at a Solution I really don't even know where to start with this. I think that aii and ajj must both be > 0 since they are on the...

I am curious if anyone knows conditions on the invertibility of a symmetric Toeplitz matrix. In my research, I have a symmetric Toeplitz matrix with entries coming from the binomial coefficients. Any help would be appreciated. Ex: [6 4 1 0 0] [4 6 4 1 0] [1 4 6 4 1] [0 1 4 6 4] [0...

I've been working through the Linear Algebra course at MITOCW. Strang doesn't go into the Jordan form much. When a matrix A is diagonalizable then A= S \Lambda S^{-1} and the matrix S can be formed from eigenvectors that correspond to the eigenvalues in \Lambda Question: how do...

The matrix A is symmetric and tridiagonal. If B is the matrix formed from A by deleting the first two rows and columns, show that \left|A\right| = a_{}11\left|M_{}11\right| - (a_{}1)^{}2\left|B\right| where \left|M_{}11\right| is the minor of a_{}11 I know what a symmetric tridiagonal...

Hi all: I am confused that in general case, if [H,p]=0 (where H is Hamiltonian of system and P is parity operator), system wave function is either symmetric or antisymmetric. How do we know that system is in lower energy state if its wave function is symmetric by comparing that system is...

Homework Statement Given the Hamiltonian and perturbation below, what are the energy shifts for the states with l=1 Given H_{0}=(L^2)/(2I) H_{1}=E_{1}cos\vartheta Homework Equations L= r x P The Attempt at a Solution in order to find the first order correction to the energy...

If I convert a symmetric group of degree n into a metric space, what metrics can be defined except a discrete metric? If a metric can be defined, I am wondering if the metric can describe some characteristics of a symmetric group.

Homework Statement http://img266.imageshack.us/img266/152/78148531ur5.png Homework Equations A is symmetric. The Attempt at a Solution First of all if you calculate rT you'll get qTA so why it the order reversed in the picture above? Moreover I don't see why it is zero.

Homework Statement I am supposed to find out if this function is symmetric with reference to the y-axis or reference to the origin. The function is F(x)=4x^2/(x^3+x) Homework Equations These are how to know if even or odd A(-x)^even power = ax^even power A(-x)^odd power = -ax^odd power The...

Give an example of a 2X2 symmetric matrix B that cannot be written as B = ATA. Give an explanation as to why no such A exists for the matrix B you have given. I know that the product ATA is a symmetric matrix, but how could there be no such A that exists for some matrix B? I'm really...

I am looking for a mechanism to find a decomposition of symmetric groups. For finitely generated abelian group G, there is a mechanism to decompose G such that G is isomorphic to a direct sum of cyclic groups. For symmetric groups, it seems a bit complex for me to find it. For example...

My question is; Let S = {A € Mn,n | A = AT } the set of all symmetric n × n matrices Show that S is a subspace of the vector space Mn,n I do not know how to start to this if you can give me a clue for starting, I appreciate.

Homework Statement Lemma 1: Fix the circle C with center (x nought, y nought); y nought is greater than 0 and radius R is less than y nought. Consider two points P (x nought, y noight tilde) and P prime (x nought, -y nought tilde) which are symmetric with respect to x-axis by construcion...

I was reading about the momentum-energy tensor (or stress-energy tensor), at one point the author says, " \theta^{\mu\nu} = (\partial^\mu\phi)(\partial^\nu\phi) - g^{\mu\nu}L This is clearly symmetric in \mu and \nu." \theta^{\mu\nu}: is the stress-energy tensor \phi is a scalar field...

Homework Statement Demostrate: c\cdot (A \times b) \neq (A \times b) \cdot c with A \in\Re^{3 \times 3} is a symmetric Tensor of second order and b,c \in \Re^3 are vectors Homework Equations The Attempt at a Solution (A \times b)_ {ij} = A_{ij} \epsilon _{jkl} b_l

Homework Statement A matrix S is symmetric if S = ST. Show that AAT is symmetric for any matrix A. Homework Equations AAT = (AT)TAT The Attempt at a Solution I just said: A = (AT)T and AT = AT Therefore AAT is symmetric. I am unsure if that proves it or if I just went in...

Homework Statement A cylindrically symmetric plasma column in a uniform B field (= B0 in z direction) has n(r) = n0 exp[-(r/r0)^2] and ni = ne = n0exp[e phi/kb Te] where phi is the potential and Te is the temp of the electrons. (a) Show that Ve and VDe are equal and opposite Homework...

Hi there, I would appreciate if you could share your exeriences or ideas about properties of 4x4 symmetric/hermitean matrices H such that U^T H U = D = diag( E1, -E1, E2, -E2 ) or diag (E1, E2, -E1, -E2 ) The things I would like to perform are the following - decompose an expression...

Hello, It's been a while since I've had to determine whether a relation is reflexive, symmetric or transitive so I would appreciate a bit of guidance. I now that being reflexive means the relation xRx for all x and being symmetric implies xRy and yRx for all x, y and transitive implies that if...

Homework Statement Hi, I need to prove that if S is a skew-symmetric matrix with NXN dimension and B is any square real-valued matrix, therefore the product of transpose(B), S, and B is also askew symmetric matrix Homework Equations This is what I know so far. 1.Transpose(S) = -S...

Let A in n x n real matrix. For every x in R^n we have <Ax,x>=0 where < , > is scalar product. prove that A^t=-A (A is skew symmetric matrix)

Write parametric and symmetric equations for the z-axis. I'm not sure i am on the right track; here is my attempt to an answer. [0, 0, z] where z can equal any number. a = [0, 0, 1] b = [0, 0, z] Parametric equations x = 0 y = 0 z = 1 + tz Symmetric equations...