# 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.

View More On Wikipedia.org
1. ### I Exploring the Trace of a Fourth Rank Tensor in Index Notation

What is the general expression for the trace of a fourth rank tensor? Do you sum over possibilities of contractions with some factor? So, for instance, for the Riemann tensor, it is given by: $\eta_{ab}\eta_{cd}R^{acbd}$ due to these being independent contractions due to the symmetry...
2. ### POTW Comparing Rank and Trace of a Matrix

Let ##M## be a nonzero complex ##n\times n##-matrix. Prove $$\operatorname{rank}M \ge |\operatorname{trace} M|^2/\operatorname{trace}(M^\dagger M)$$ What is a necessary and sufficient condition for equality?
3. ### POTW A Linear Operator with Trace Condition

Let ##V## be a finite dimensional vector space over a field ##F##. If ##L## is a linear operator on ##V## such that the trace of ##L\circ T## is zero for all linear operators ##T## on ##V##, show that ##L = 0##.

18. ### I Why does the trace show up while computing unpolarized cross sections?

I've been studying different scattering processes (from Mandl & Shaw QFT's book, chapter 8) and there's always a common step I do not understand: the showing-up of the trace. Let me give two specific examples. Lepton Pair Production ##( e^+ (\vec p_1, r_1) + e^- (\vec p_2, r_2) \rightarrow l^+...
19. ### I Trace of the stress energy tensor

The stress energy tensor has many forms based on the type of matter you are describing, dust, fluid, perfect fluid... is it true that the trace of all of these matter situations is invariant?
20. ### I Taking a partial trace of a multipartite state for measurement

I am attempting to understand how POVMs fit in with quantum measurement, and I think I am getting tripped up in notation when it comes to multipartite systems. The situation is as follows: System: \rho_A Measurement instrument: \rho_B = |\phi\rangle\langle\phi| (pure state) The multipartite...
21. ### A Trace of a product of Dirac Matrices in a Fermion loop

I'm working out the quark loop diagram and I've drawn it as follows: where the greek letters are the Lorentz and Dirac indices for the gluon and quark respectively and the other letters are color indices. For this diagram I've written...
22. ### Fluke PM3384A combiscope trace fault

I’ve just bought this useful looking 100 MHz scope in the hope of repairing it. When I switch to digital mode, the trace disappears off-screen on all four channels. 1 and 3 are up high, 2 and 4 down low. Sometimes the top or bottom of the trace is visible, and it flickers up and down the...
23. ### Trace of a subsystem of a two qubit system

Consider the first qubit (subsystem A): First, the density operator for the system AB is ## \rho ^{AB} =\frac { \left |00 \right > \left <00 \right |+ \left |01 \right > \left < 01\right |+\left | 11\right > \left < 11\right | } 3 ##. Then, the reduced density operator of subsystem A is ##...

43. ### A Expectation values and trace over the environment

I've worked through a Stern Gerlach experiment for the Sx and Sz directions using the density matrix formalism to account for the environment. This shows a result which I think is correct but relies on decoherence to give the "actual" value. I'm not confident about the result though. Would...
44. ### Dirac Trace Algebra: Which Gamma Matrices Matter?

Homework Statement This isn't a homework problem; it's just something I'm working on and I'm a little confused as to how to go about dealing with what I have. I have several traces of Dirac's gamma matrices, and I know that the trace of an odd number of gamma matrices is zero. So my first...
45. ### Trace of cathode ray in changing magnetic field.

I know that cathode rays follow a helical pattern if they enter a uniform magnetic field at an angle less than 90 degrees. This leaves me with two questions. 1. If the cathode ray described above, hit a phosphor coated screen, would it show only 1 spot or a circle? 2. If the magnetic field was...
46. ### What is the trace of a second rank covariant tensor?

What is the trace of a second rank tensor covariant in both indices? For a tensor covariant in one index and contravariant in another ##T^i_j##, the trace is ##T^k_k## but what is the trace for ##T_{ij}## because ##T_{kk}## is not even a tensor?
47. ### Zettili QM Problem on Trace of an Operator

Homework Statement In Zettili's QM textbook, we are asked to find the trace of an operator |\psi><\chi| . Where the kets |\psi> and |\chi> are equal to some (irrelevant, for the purposes of this question) linear combinations of two orthonormal basis kets. Homework Equations...
48. ### Entanglement, projection operator and partial trace

Homework Statement Consider the following experiment: Alice and Bob each blindly draw a marble from a vase that contains one black and one white marble. Let’s call the state of the write marble |0〉 and the state of the black marble |1〉. Consider what the state of Bob’s marble is when Alice...
49. ### Setting the trace of a tensor equal to zero

Homework Statement A tensor t has the following components in a given orthonormal basis of R3 tij(x) = a(x2)xixj + b(x2) \deltaij x2 + c(x2) \epsilonijk xk (1) where the indices i,j,k = 1, 2, 3. We use the Einstein summation convention. We will only consider orthogonal transformations...
50. ### How do I calculate the trace of SU(3) generators in the adjoint representation?

Hi all, The trace of two SU(3) generators can be calculated by: ## T_{ij} T_{ji} = \frac{1}{2} ##, now how to calculate the trace of SU(3) generators: ## T_{il} T_{lk} T_{kj} T_{ji} ## ?