Trace Definition and 190 Threads

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) =...

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...

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

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...

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?

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}...

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

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...

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

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...

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...

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}

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...

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...

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...

I am looking for a good book , for 'pedestrian (aka Dummies ) introduction to noncommutative geometry and another book about Selberg Trace. I am a physicist, hence perhaps my math knowledge is not high i know - a bit of differential geometry - Calculus (real and complex) - Quantum...

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

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

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...

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...

Homework Statement How do I get the expectation value of operator \sigma using density matrix \rho in a trace: Tr\left(\sigma\rho\right) I have \sigma and \rho in matrix form but how do I get a number out of the trace?

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...

I understand the definition of trace and linear operator individually but I don't seem to understand as to what does it mean by trace of a linear operator on a finite dimensional linear space. What I have found out is that trace of a linear operator on a finite dimensional linear space is the...

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)...

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

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...

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...

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?

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

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...

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

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...

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...

How far back can you trace your ancestors ?

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...

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...

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)...

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

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...

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