What is Symmetric: Definition and 563 Discussions

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music.This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry, which refers to the absence or a violation of symmetry.

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  1. P

    I Conditions for Spherically Symmetric Black Hole Solution

    What is the condition for a spherically symmetric solution represents a black hole? ##ds^2=\exp(\nu(r))dt^2-\mu(r)^{-1}dr^2-r^2 d\Omega^2## it is enough that it is fulfilled that ##\nu## and ##\mu## are nulled in the same value of r??. There are other conditions?
  2. Rodrigo

    ANSYS APDL 18.2 - Symmetric Stiffened Plate

    Hello, I'm a new ANSYS user and could someone give me some help about this tutorial: https://confluence.cornell.edu/display/SIMULATION/ANSYS+-+Semi-monocoque+shell+-+Problem+Specification I'm trying to replicate it but can't get the same answear in the end. Any advice about what i could do...
  3. F

    I Symmetric and Antisymmetric Wavefunction

    Hello, My understanding is that, for a multi-particle system, the overall wavefunction HAS to be either symmetric or antisymmetric. A wavefunction that is neither symmetric or antisymmetric must be converted into one that is one of the two types depending on the type of particles. For example...
  4. Phi6er

    A I need a spherically symmetric spin-dependent NN potential

    First, I'll give a little background so you guys know why I've arrived at this issue. I'm writing my BSc thesis right now, and the point of the thesis is to predict the bound states of two-nucleon systems (one bound, others not) by treating the problem as a simple QM two body problem. With a...
  5. binbagsss

    I Are spherically symmetric and isotropic the same

    If space-time is isotropic does this imply it is spherically symmetric? why doesn't it need to be both isotropic and homogeneous?
  6. A

    Stiffness matrix for a symmetric structure

    Good day All While trying to solve the following exercice, I was stucked by a couple of issues for the first part in which we have to find the simplest configuration ( symmetry) according to my basic understanding Symmetry must be : geometry load support here I don t have the third...
  7. C

    I Splitting ring of polynomials - why is this result unfindable?

    Assume that ##P## is a polynomial over a commutative ring ##R##. Then there exists a ring ##\tilde R## extending ##R## where ##P## splits into linear factor (not necessarily uniquely). This theorem, whose proof is given below, is difficult to find in the literature (if someone know a source, it...
  8. L

    A Tensor symmetries and the symmetric groups

    In one General Relativity paper, the author states the following (we can assume tensor in question are tensors in a vector space ##V##, i.e., they are elements of some tensor power of ##V##) To discuss general properties of tensor symmetries, we shall use the representation theory of the...
  9. ubergewehr273

    Non symmetric case of Ampere's law

    When we use Ampere's law, the most basic case that of an infinite current carrying wire is taken whose magnetic field is evaluated at a distance r from the wire. However there's nothing wrong in using the law for non symmetric scenarios. If this is the case how do you explain the B field at a...
  10. Y

    MHB Symmetric and invertible matrix

    Hello all, If A and B are both squared invertible matrices and A is also symmetric and: \[AB^{-1}AA^{T}=I\] Can I say that \[B=A^{3}\] ? In every iteration of the solution, I have multiplied both sides by a different matrix. At first by the inverse of A, then the inverse of the transpose...
  11. S

    A How can the LRS model for leptons incorporate the Standard Model group?

    This is a homework problem in a course in particle physics at Cornell University. Assume the Left Right Symmetric (LRS) model for leptons. The gauge group is GLR = SU(2)L×SU(2)R×U(1)X. The Standard Model group SU(2)L×U(1)Y has to be included in the LRS group. Namely, U(1)Y ⊂ SU(2)R×U(1)X. Find...
  12. H

    A Geodesic Distance & Maximally Symmetric Spacetimes: Why Does it Matter?

    Any physical quantity ##K(t,x,x')## on a maximally symmetric spacetime only depends on the geodesic distance between the points ##x## and ##x'##. Why is this so? N.B.: This statement is different from the statement that The geodesic distance on any spacetime is invariant under an arbitrary...
  13. riveay

    Euler angles in torque free precession of a symmetric top

    Is calculating the Euler angles analitically possible? I am trying to obtain the angles to transform the body-fixed reference frame to the inertial reference frame. I can get them without problems with numerical methods. But I would to validate them analitically, if possible. I followed the...
  14. L

    I Relativistic field of moving charge. Why is it symmetric?

    Hi people! First of all, sorry for my poor english. I read in many places and I did the calculus and I agree that the field of a moving charge have this aspect: (Taked from Feynman´s Lectures on Physics chapter 26th.) But my problem is in that my intuition says me that it must be something...
  15. M

    What is the derivative of a skew symmetric matrix?

    Homework Statement Need to prove that the derivative of a rotation matrix is a skew symmetric matrix muktiplied by that rotation matrix. Specifically applying it on the Rodrigues’ formula.Homework EquationsThe Attempt at a Solution I have shown that the cubed of the skew symmetric matrix is...
  16. R

    Is a symmetric charge distribution the lowest potential

    Is the potential energy of a symmetric planar (x,y) charge distribution lower than any non symmetric distribution ? from the discussion on Gauss's law and symmetric charge distributions I would think so because the electric field could only be normal to the (x,y) plane in the symmetry case but...
  17. davidge

    I Is the FLRW Metric the Only Form for One-Dimensional Maximally Symmetric Spaces?

    I have a question regarding the FLRW metric used for cosmological analysis in S & G Relativity. Let the coordinates of a point in the space time be ##(t,r,\theta,\varphi)##. For constant ##t, \theta## and ##\varphi## we have the metric $$d \tau^2 = \frac{dr^2}{1 - kr^2}$$ My doubt is about this...
  18. R

    I If symmetric then transitive relation

    Isn't, if we have xRy and yRx then xRx will also make transitive? Because if I am right {(x,x),(y,y)} on set {x,y} is symmetric and transitive. Isn't the above similar to, if xRy and yRz then xRz is transitive relation? Thanks.
  19. S

    Can transformation coefficients be interchanged in symmetric tensors?

    Homework Statement The lecture notes states that if ##T_{ij}=T_{ji}## (symmetric tensor) in frame S, then ##T'_{ij}=T'_{ji}## in frame S'. The proof is shown as $$T'_{ij}=l_{ip}l_{jq}T_{pq}=l_{iq}l_{jp}T_{qp}=l_{jp}l_{iq}T_{pq}=T'_{ji}$$ where relabeling of p<->q was used in the second...
  20. N

    B Why is state transition probability symmetric?

    Restricting to finite dimensional QP, suppose a system is in a state S1, an experiment is done, and state S2 is one of the eigenstates (assume all eigenvalues are distinct). The probability that the system transitions from S1 to S2 is p = Trace( S1*S2), using state operator notation. On the...
  21. F

    I Symmetric, antisymmetric or neither

    Hello, If a composite system is formed by particles that are all fermions, the overall wavefunction must be antisymmetric. If the particles are all bosons, the wavefunction must be symmetric. What if the particles are not all identical particles (all electrons) but are all fermions? Does the...
  22. thenewmans

    B What’s the difference between TIQM and Time Symmetric QM? (a

    I have a few questions about interpretations that use retrocausality. I only know of 2. 1. TIQM - Transactional Interpretation of QM by John Cramer 1986 https://en.wikipedia.org/wiki/Transactional_interpretation 2. TSQM - Time Symmetric QM by Huw Price...
  23. T

    I Seesaw Mechanism of vMSM and Left Right Symmetric Extension

    I know the seesaw mechanism is a model used to explain both neutrinos having mass and why their dirac mass/yukawa coupling is so much smaller than for the other fermions. The seesaw mechanism needs the right handed neutrino to exist. How does the seesaw mechanism for the vMSM differ from that...
  24. S

    I A _perfectly_ symmetric twin paradox cases

    Case 1) Two rockets (no Earth involved) have an exactly the same acceleration profile/flight-plan during round trip but they dispatched to opposite directions. At the start both rockets are docked to the same space station...both rockets have an identical engine operation plan during the round...
  25. T

    What is the definition of a function being spherically symmetric?

    Homework Statement Hi guys, having problem trying to understand what this question wants. the question I am stuck with is 7.3. Homework EquationsThe Attempt at a Solution So for a) I converted to spherical co-ordinates: ##log(r^2sin^\theta cos^2\phi+r^2sin^2\theta sin^2\phi+r^2...
  26. T

    I Left Right Symmetric Extension of SM and vMSM

    Hello. Im trying to learn more about different extensions of the standard model. Are the Left Right Symmetric Extension of the Standard model and the Neutrino Minimal Standard Model different extensions? I know both add 3 right handed neutrinos. Do these neutrinos differ in any way, also are...
  27. Y

    MHB Is the Symmetric Difference Problem Solved?

    Hello all, For each of the following statements, I need to say if it is true or not, to prove if it is true or to contradict if not. 1) \[A\bigtriangleup (B\cap C)=(A\bigtriangleup B)\cap (A\bigtriangleup C)\] 2) \[A\cup (B\bigtriangleup C)=(A\cup B)\bigtriangleup (A\cup C)\] Where...
  28. Mr Davis 97

    Show that the symmetric group S_n has elements of all order

    Homework Statement Prove that if ##1 \leq d \leq n##, then ##S_n## contains elements of order d. Homework EquationsThe Attempt at a Solution Here is my idea. The order of the identity permutation is 1. Written in cycle notation, the order of (1,2) is 2, the order of (1,2,3) is 3, the order of...
  29. F

    Symmetric positive definite

    Homework Statement Here's the question : 1x1+ 2x2 +0x3 + 0x4 = 1 2x1+ 9x2 +1x3 + 0x4 = 6 0x1+ 1x2 +9x3 + 4x4 = 2 0x1+ 0x2 +4x3 + 3x4 = 8 I' m asked to solve this question using Choelsky method ( We need the symmetric positive definite matrix when we are using this method) Homework...
  30. Yiming Xu

    I Express power sums in terms of elementary symmetric function

    The sum of the $k$ th power of n variables $\sum_{i=1}^{i=n} x_i^k$ is a symmetric polynomial, so it can be written as a sum of the elementary symmetric polynomials. I do know about the Newton's identities, but just with the algorithm of proving the symmetric function theorem, what should we do...
  31. F

    Symmetric loading vs antisymmetric loading

    Homework Statement For the circled beam , we can see that for both cases , the load are loaded in the same way ... Why the M / EI diagram for the first case is different from the second case ? Why for the first case , it's symmetric loading ? For the second case , it's antisymmetric loading ...
  32. itssilva

    Lack of evidence for symmetric partners and extended spacetime?

    Some motivation: It's relatively easy to postulate "supersymmetric theories" - e.g., you can build one by simply monkeying around with the harmonic oscillator H = p2+x2 and linear combinations of x and p using Grassmann numbers - that, AIU, is NOT what one usually refers to as SUSY, but...
  33. L

    MHB Proving Reflexive, Symmetric and Transitive Properties of Relation R on P(U)

    Let U be a universal set, and let C be any subset of U. Let R be the relation on P(U) defined by A R B if $A \cap C = B \cap C$. Determine whether the relation is reflexive, symmetric, and/or transitive. Prove you answer.
  34. TeethWhitener

    I Is a symmetric matrix with positive eigenvalues always real?

    I split off this question from the thread here: https://www.physicsforums.com/threads/error-in-landau-lifshitz-mechanics.901356/ In that thread, I was told that a symmetric matrix ##\mathbf{A}## with real positive definite eigenvalues ##\{\lambda_i\} \in \mathbb{R}^+## is always real. I feel...
  35. N

    I Symmetric, self-adjoint operators and the spectral theorem

    Hi Guys, at the moment I got a bit confused about the notation in some QM textbooks. Some say the operators should be symmetric, some say they should be self-adjoint (or in many cases hermitian what maybe means symmetric or maybe self-adjoint). Which condition do we need for our observables...
  36. V

    I Linear algebra ( symmetric matrix)

    I am currently brushing on my linear algebra skills when i read this For any Matrix A 1)A*At is symmetric , where At is A transpose ( sorry I tried using the super script option given in the editor and i couldn't figure it out ) 2)(A + At)/2 is symmetric Now my question is , why should it be...
  37. karush

    MHB S4.854.13.5.47 Find symmetric equations, angle between the planes

    $\tiny{s4.854.13.5.47}$ $\textsf{a. Find symmeteric equations for the line of intersection of planes}\\$ $\textsf{b. Find the angle between the planes}\\$ \begin{align}\displaystyle j+y-z&=2 \\ 3x-4y+5z &=6 \end{align} \begin{align}\displaystyle n_1&=\langle 1,1,-1\rangle\\ n_2&=\langle...
  38. F

    MHB Cartesian product and symmetric difference

    Let A,B,C be three sets . Prove Ax(BΔC)= (AxB) Δ (AxC) I tried to start with this : Let p be an arbitrary element of Ax(BΔC) then p=(x,y) such that x ∈ A and y ∈ (BΔC) x ∈ A and (y∈ B\C or y∈ C\B) (x ∈ A and y ∈ B\C) or (x ∈ A and y ∈ C\B) But I don't know how to continue or if I should even...
  39. D

    Electrostatic polarization of an axially symmetric conductor

    Homework Statement A grounded Z-axis symmetric closed conductor has a single point charge at the origin within it, inducing negative charge onto its inner surface. Given the induced charge density from the unit point charge, find the surface charge induced instead by a unit dipole at the...
  40. S

    Symmetric square well, wavefunction is weird

    Hi, I'm trying to work my way through some problems and am stuck on one for a symmetric infinite square well, of width 2a, so -a<x<+a. Since this is the symmetric case, the wavefunction should be a linear combination of the terms (a)-½ cos (nπx/2a) for odd n, (a)-½ sin (nπx/2a) for even n...
  41. M

    I Relationship Between Hermitian and Symmetric Matrices

    Are All symmetric matrices with real number entires Hermitian? What about the other way around-are all Hermitian matrices symmetric?
  42. Mr Davis 97

    Prove that diagonal matrices are symmetric matrices

    Homework Statement Same as title. Homework EquationsThe Attempt at a Solution A defining property of a diagonal matrix is that ##A_{ij} = A_{ji} ~~\forall i,j \le n##. This means that ##((A)^{t})_{ji} = A_{ji}##. Therefore, we know that ##A^t = A##. This shows that a diagonal matrix is...
  43. Elvis 123456789

    B How do you know a force if a force is radially symmetric?

    If a force only depends on a radial distance "r" and it only has a radial component in the "er" then is it radially symmetric? This pertains to some homework problem I have, but part of the problem is that I'm not exactly sure what is meant by "radially symmetric". I assume its asking if the...
  44. K

    I Why is the s state spherically symmetric?

    Hi there, I am reading something about quantum numbers, there the author introduce the quantum number by solving Schrodinger equation for Hydrogen atom. It gives me an example when the principal quantum number n=4, there are four different sub-level ##s, p, d, f##. It also depicts the sublevel...
  45. F

    Gauss's law and symmetric charge distributions

    Having read several introductory notes on Gauss's law, I have found it very frustrating that when the author comes to discussing the standard examples, in which one considers symmetric charge distributions, they do not explicitly discuss the symmetries of the situation, simply stating that, "by...
  46. gasar8

    Spherical Symmetric Harmonic Oscillator

    Homework Statement An electron (S=1/2) is free in a spherical symmetric harmonic potential: V(r)=\frac{1}{2}kr^2 a) Find energies and degeneracy of ground state and first excited state. b) For these states find the l^2 and l_z basis. c) How does these states split in a \vec{L} \cdot \vec{S}...
  47. SuperSusanoo

    Proof about symmetric groups and generators

    Homework Statement Let n>=2 n is natural and set x=(1,2,3,...,n) and y=(1,2). Show that Sym(n)=<x,y> Homework EquationsThe Attempt at a Solution Approach: Induction Proof: Base case n=2 x=(1,2) y=(1,2) Sym(2)={Id,(1,2)} (1,2)=x and Id=xy so base case holds Inductive step assume...
  48. P

    MHB Sava's question via email about symmetric matrices

    A matrix is symmetric if it is equal to its own transpose, so to show $\displaystyle \begin{align*} C^T\,C \end{align*}$ is symmetric, we need to prove that $\displaystyle \begin{align*} \left( C^T\,C \right) ^T = C^T\,C \end{align*}$. $\displaystyle \begin{align*} \left( C^T\,C \right) ^T &=...
  49. B

    Prove 3x3 Skew symmetric matrix determinant is equal to zero

    Homework Statement Hi there, I'm happy with the proof that any odd ordered matrix's determinant is equal to zero. However, I am failing to see how it can be done specifically for a 3x3 matrix using only row and column interchanging. Homework Equations I have attached the determinant as an...
  50. M

    Cylindrical symmetric magnetic field

    Homework Statement Suppose the magnetic field line pattern is cylindrical symmetric. Explain with Stokes theorem that the field decreases like 1/r (with r the distance from the axis of the cylinder). Homework Equations Stokes theorem The Attempt at a Solution I was thinking of a circular loop...
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