What is Trace: Definition and 197 Discussions

Transition Region and Coronal Explorer (TRACE) was a NASA heliophysics and solar observatory designed to investigate the connections between fine-scale magnetic fields and the associated plasma structures on the Sun by providing high resolution images and observation of the solar photosphere, the transition region, and the corona. A main focus of the TRACE instrument is the fine structure of coronal loops low in the solar atmosphere. TRACE is the fourth spacecraft in the Small Explorer program, launched on April 2, 1998, and obtained its last science image on 21 June 2010 23:56 UT.The satellite was built by NASA's Goddard Space Flight Center. Its telescope was constructed by a consortium led by Lockheed Martin's Advanced Technology Center. The optics were designed and built to a state-of-the-art surface finish by the Smithsonian Astrophysical Observatory (SAO). The telescope has a 30 cm (12 in) aperture and 1024×1024 CCD detector giving an 8.5 arc minute field of view. The telescope is designed to take correlated images in a range of wavelengths from visible light through the Lyman alpha line to far ultraviolet. The different wavelength passbands correspond to plasma emission temperatures from 4,000 to 4,000,000 K. The optics use a special multilayer technique to focus the difficult-to-reflect EUV light; the technique was first used for solar imaging in the late 1980s and 1990s, notably by the MSSTA and NIXT sounding rocket payloads.

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  1. Borek

    What planes are flying over Europe right now?

    Well, not every plane, just those equipped with ADS-B. Still, fun to check what it is flying over your house. http://www.flightradar24.com/
  2. C

    Trace formula in noncommutative geometry and the Riemann hypothesis

    Does anyone know where to find this paper? Formule de trace en géométrie non-commutative et hypothèse de Riemann = Trace formula in noncommutative geometry and the Riemann hypothesis http://cat.inist.fr/?aModele=afficheN&cpsidt=2561461 The purchase link is broken there.. it gets stuck...
  3. homology

    Is the trace of a linear operator independent of orthonormal basis?

    Hi, I came across a line (http://www.springerlink.com/content/t523l30514754578/) about how the trace of a linear operator is not, in general, independent of the choice of orthonormal basis. The link states that such an operator may have a trace that converges for one basis but not another...
  4. G

    Proving Uniqueness of Trace Function on n X n Matrices

    Homework Statement Show that the trace functional on n X n matrices is unique in the following sense. If W is the space of n X n matrices over the field F and if f is a linear functional on W such that f(AB) = f(BA) for each A and B in W, then f is a scalar multiple of the trace function. If...
  5. D

    Finding the Trace of a Product of 4 SL(2,C) Matrices | Helpful Guide

    Dear All I'd be very grateful if someone could help me out with finding the trace of a product of 4 SL(2,C) matrices, namely: \mathrm{Tr} \left[ \sigma^{\alpha} \sigma^{\beta} \sigma^{\gamma} \sigma^{\delta} \right] where: \sigma^{\alpha} = (\sigma^0, \sigma^1, \sigma^2, \sigma^3)...
  6. C

    Trace of a matrix and an expansion of eigenvectors

    Hi, I'm trying to derive the Kullback-Leibler divergence between two multi-variate gaussian distributions, and I need the following property. Is there a simple way to understand this? Prove that: Given that E has orthonormal eigenvectors u_{i} and eigenvalues \lambda_{i} Then: trace(A*E) =...
  7. Z

    What is the Definition of a Trace and Can it Prove the Riemann Hypothesis?

    the idea is this, for the mathematician what is exactly the definition of a Trace ?? for example let us suppose that i find a trace operator for Riemann Zeros, then would it mean that i have solved Riemann Hypothesis ?? In the paper...
  8. L

    Using Trace to Determine Orthogonality of Matrices

    Is there a way to use the trace of a matrix to find whether a set of matrices are orthogoal to one another?
  9. T

    Proving trace of (1,1) Tensor is a scalar

    Homework Statement Given a tensor Mab, Prove that its trace is a scalar. Homework Equations The Attempt at a Solution To prove the trace is a scalar, I know I have to prove it doesn't transform under coordinate transformations. Now, we can transform M^a_b as follows...
  10. Somefantastik

    Is the Jacobian Matrix for an Equilibrium Point Unstable?

    Hello, I have a Jacobian matrix A = \left( \begin{array}{cc} -2x+1-a_{1}y & -a_{1}x \\ -a_{2}ry & r-2ry-ra_{2}x \end{array} \right)\ where a_{1} > 1 \ ; \ a_{2} > 1 \ ; \ and \ r>0 the trace is Tr(A) = 1-2x-a_{1}y+r(1-y-a_{2}x)-ry = x(-2-ra_{2}) +y(-a_{1}-2r)+1+r ...
  11. P

    What is the trace of the second-Rank tensor?

    In Lorentz group in QFT, why the trace of the symmetric second-Rank tensor S^{\mu\nu} is defined as follows? S=g_{\mu\nu}S^{\mu\nu}. Is it just a definition or the genuine trace of the second-Rank tensor, and why?
  12. malawi_glenn

    The Gamma Matrix Trace Paradox: A Conundrum in Spinor Calculations

    gamma matrix trace Paradox?? Hello, i tried to evaluate this particular little guy: \text{Tr} (\gamma ^0 p_\mu \gamma ^\mu \gamma ^0 q_\nu \gamma ^\nu ) using these identities: \gamma^0 \gamma^0 = I \text{Tr} (\gamma^\mu \gamma^\nu \gamma^\rho \gamma^\sigma) = 4 (g^{\rho \sigma} g^{\mu \nu}...
  13. S

    Trace of a matrix equals sum of its determinants?

    If a matrix is diagonalizable, how does its trace equal the sum of its eigenvalues? I can't find a proof for this anywhere.
  14. Peeter

    What is the purpose of trace in quantum mechanics?

    Reading Quantum Mechanics Demystified, and trace of an operator is covered. This includes how to compute it if one has the matrix of an operator, or how to compute it given the outer product representation of an operator. There is however, no mention of what such a trace would be used for...
  15. A

    Trace and Determinant Relationship: Proving the Relation with O(x^2)

    Hi, can anyone give me an hint to proof the relation det(I + x A) = 1 + x tr A + O(x^2) thank you.
  16. B

    Partial Trace For Tripartite Systems

    Dear All, Base on "Problems and Solutions in Quantum Computing and Quantum Information" book I can understand and compute partial trace for bipartite. Now I'm trying to understand partial trace for tripartite system but I still not get good references or equation. Anybody can help me to get...
  17. K

    Trace the path of the light ray and find angle of refraction

    Homework Statement A ray of light strikes the midpoint of one face of an equiangular (60◦, 60◦, 60◦) glass prism (n = 1.3) at an angle of incidence of 33◦. a.Trace the path of the light ray through the glass, and find the angle of refraction at the first surface. b.Find the angle of...
  18. JasonJo

    Taking the Trace of a Tensor Product

    Hey guys, How exactly do you take the trace of a tensor product? Do I take the trace of each tensor individually and multiply their traces? For example, how would I take the trace of this tensor product: -B^{c}_b B_{ac}
  19. G

    Linear Algebra Question (Trace)

    I am trying to simplify the following, so that I can differentiate it (with respect to X). Ideally I'll have everything in terms of (XX^T - YY^T). \mathrm{trace}[(AX(AX)^T)((BX)(BX)^T)^{-1}] - \mathrm{trace}[(AY(AY)^T)((BY)(BY)^T)^{-1}] Where X and Y are 3 x N and A and B are N x N...
  20. T

    What this function does(i tried to trace it

    i understand what each line does here but i can't see what this function does in general?? typedef struct node node; //node is alias for struct node struct node{ int value,count; node *lc,*rc; }; node *what(node *tree){ node...
  21. T

    Finding the range of the trace

    Homework Statement Find the basis for the range of the following transformation: T(A)=tr(A) Homework Equations tr(A)=a(1,1)+a(2,2)+...+a(n,n) {not a multiple of but just subscripts of the entries of the diagonal elements} The Attempt at a Solution Since the elements can be...
  22. M

    Books on Selberg Trace /Noncommutative geometry

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  23. M

    Connes Trace and Its Relation to Riemann Hypothesis: An Overview

    What is the so called Connes trace and its relation to Riemann Hypothesis proposed by the physicist COnnes ? , or in fact how it would be related to Riemann Hypothesis
  24. J

    Is partial trace still cyclic?

    Hello, I know trace is usually cyclic, but is partial trace cyclic too? Why? Thanks! Jenga
  25. S

    Eqn of Plane passing through a point and perpendicular to another plane's trace

    Homework Statement Here's the problem:Find the equation of the plane passing through the point (-3,1,4) and perpendicular to the trace of the plane x-3y+7z-3=0 in the xy plane. Homework Equations to me this should be as easy as finding the two coordiates of the plane's traces on the x...
  26. V

    A question about trace technology

    Hi everybody! While reading Peskin-Schroeder, i stuck in the in equation 5.4 about the unpolarized cross section of the e^- e^+ \rightarrow \mu^- \mu^+ annihilation. i didn't understand how this relationof the electron trace came to be, and where the indices came from...
  27. C

    Expectation values and trace math

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  28. P

    Field trace and norm (Equivalence between definitions)

    I'm sure whoever is familiar with this subject has already seen this several times. I've seen it several times myself, and I even remember proving it in detail a couple of years ago, but now I'm stuck. I'm quoting what my professor did in class. Given some separable extension L/K, say for...
  29. S

    Trace of a linear operator

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  30. T

    Selberg formula for trace.

    Could someone explain the 'Selberg Trace formula' concept?? for example let be the Laplacian in curved Space-time: \Delta \Psi = E_{n} \Psi My question is is there a relationship between the set of eigenvalues E(n) and a certain charasteristic of the SUrface (length, Areal or so on)...
  31. P

    Trace of gamma matrices with FORM

    Hello everybody, I have to calculate the matrix element of the process gg-->ttbar-->lnub lnub (ttbar dileptonic decay) using FORM. I have three feynman dyagrams for such a process. When I calculate the interference term i have as output thousands of terms with Levi civita tensors inside (but...
  32. K

    What is the Concept of Zero Double Trace in Tensor Analysis?

    Hello all, I have recently encountered a tensor which is said to have the property "zero double trace". I am unfamiliar with the concept of a double trace and was hoping someone here could help. Thanks
  33. T

    DOes the trace determine the Hamiltonian

    if we define Z as: Z(s)=Tr[exp(-sH)] my 2 questions are.. a) is the trace unique and define the Hamiltonian completely? i mean if we have 2 Hamiltonians H and K then Tr[exp(-sH)]\ne Tr[exp(-sK) and if we use the 'Semiclassical approach' then Z(s)=Tr[exp(-sH)]\sim...
  34. B

    Understanding the Trace Theorem in Calculating S-Matrix | QFT Explained

    Hi guys, Everyone knows that one can calculate the S-Matrix with various tricks. One of them is to use traces to simplify the matrices. Can someone tell me or point me to a place where I can find an explanation why I can do this? I think I vaguely remember that I have seen once an...
  35. W

    Ricci Tensor & Trace: Exploring the Relationship Between Tensors & Traces

    Just wondering if Traces can be applied to tensors. If the Ricci tensor is Rii then is sums over diagonal elements. So technically, can you say the trace of the Riemann tensor is the Ricci tensor?
  36. D

    Finding Eigenvalues to Prove trace P is Nonnegative Integer

    I'm having trouble with this: Prove that if P is a linear map from V to V and satisfies P^2 = P, then trace P is a nonnegative integer. I know if I find the eignevalues , their sum equals trace P. But how do I find them here? any thoughts? Thanks
  37. F

    Deriving QFT Equations using Gamma Trace: A Step-by-Step Guide

    Hello, I think I need the following for a QFT problem.tr(\gamma^{5}\gamma^{\mu}\gamma^{\alpha}\gamma^{\beta}\gamma^{\nu}\gamma^{\rho}\gamma^{\sigma}) I know that...
  38. S

    Creating a Trace Bar to Track SWF Loading Progress

    How do you display a trace bar which shows how much of the swf has loaded ? Thank you
  39. D

    Max Trace of U(N) Matrices: A Complex Problem

    Assume A is a complex N \times N matrix. It is well known that \max_{V \in U(N)} |Tr(AV)| = Tr(\sqrt{AA^{\dagger}}). But what is \max_{V \in U(N)} Re(Tr(AV)) ? U(N) is the group of unitary N \times N matrices. (I could not preview my post properly, so I apologize for any...
  40. A

    Calculating Trace of 4x4 Matrix: (A+I)^{-1}

    Hello, I have to calculate the trace of the following matrix: (A+I)^{-1} where A is: 1 0 0 1 0 2 2 0 0 2 2 0 1 0 0 1 and I is the unit matrix 4x4. The calculations are extremely excruciating and the result is 38/15 [checked]. I'm afraid I miss the whole point of this. Can the...
  41. wolram

    How far back can you trace your ancestors ?

    How far back can you trace your ancestors ?
  42. R

    Trace in statistical mechanics

    Hi, I am just starting a 3rd year course in Statistical Mechanics, and am a bit confused about the operator trace, Tr. I know there is a trace for quantum operators, as well as one in classical physics, but i am not sure how to calculate either, or their physical meaning. Any help would be...
  43. C

    Similarity - trace and determinant

    What exactly is the relationship between the trace/determinant of two matrices with regards to similarity. I always thought that if the trace was the same, then there is a possibility that the matrices are similar and if the determinant was the same, then the matrices are similar. On a recent...
  44. W

    Proofs of Symmetrized Trace of F^4 for Non-Abelian Gauge Field

    my question is pretty technical, in the course of studying the non-abelian Born-Infeld, i have tried to write out the Born-Infeld langrangian written using the symmetrized trace formalism, i have met at the fourth order of field strength the term sTr(F^4)...
  45. Z

    Trace an IP in a Yahoo Chat Room?

    is there any way for someone to put an ip trace on you from a yahoo chat room i.e. public game chat room?
  46. N

    Why logic and reason fail when we try to trace back the origin of universe

    Why logic and reason fail when we try to trace back the origin of universe! When we try to think what might have created the universe,when was it created,how,why,where etc etc, the parameters we are looking at are TIME when we say WHEN and SPACE when we say WHERE,HOW,WHAT,WHO. Out of the ten...
  47. S

    What is the Trace Theorem? Calc I Seminar

    I am only in Calc I, and i am going to go to a math seminar on Trace theorem tommorow. And i was curious in simple terms, what it is and what it is used for. Thanks, Steven
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