Identity Definition and 1000 Threads

Can somebody show me how \epsilon_{mni}a_{n}(\epsilon_{ijk}b_j c_{k}) Turns in to \epsilon_{imn}\epsilon_{ijk}a_{n}b_j c_{k} Something about the first \epsilon I'm not seeing here when the terms are moved around.

I'm looking for a source online that gives the step by step derivation of common trig identities, such as sin(2theta) = 2sin(theta)cos(theta), cos(2theta) = cos2(theta)-sin2(theta), sin2(theta) = (1 - cos(2theta))/2, ect. I did do 20 minuntes or so of searching online, nothing was exactly what I...

I need to verify this identity: (A\B)\DeltaC = (A\DeltaC)\Delta(A\bigcapB) (with delta standing for the symmetric difference, I don't know the proper latex code) I've tried it "brute force" several times, working out each side and simplifying it until the sides are equal (it's likely that I'm...

Homework Statement \frac{sin\theta}{1-cos\theta} - \frac{cot\theta}{1+cos\theta} = \frac{1-cos^{3}\theta}{sin^{3}\theta} Homework Equations Trig identities.. The Attempt at a Solution Basically I got to: \frac{sin\theta+(cos^{2}\theta)(sin\theta)}{sin^{2}\theta} Homework...

This is related to differential equations, but I think my question has more to do with log identities than DE. I keep seeing equations like 1/8 lny = t + c simplified to get the solution y = ce^8t but I am unsure of the identity being used to get 1/8 into the exponent as 8. I...

In the following question I figure that i need to prove that h holds true with the trigonometric identity subbed into the denominator. I'm not sure how to simplify the equation any further after that though. Can someone provide any insight...

Hello matrices masters, If A and B are nxn square matrices, is there an identity for the determinant of the block matrix A -B B A ? Lots of thanks and praises.

Homework Statement Show that \frac{1}{2}\frac{\mathrm{d} ^{2}}{\mathrm{d} t^{2}}\int_{V}\rho x^{j}x^{k}dV = \int_{V}T^{jk}dV .Homework Equations The Attempt at a Solution \partial _{t}T^{t\nu } = -\partial _{i}T^{i\nu } from conservation of energy - momentum...

Hello, how can i prove by "fierzing" twice that (\bar{\lambda} \gamma_5 \lambda) \lambda = - (\bar{\lambda} \lambda) (\gamma_5 \lambda)? Thanks

What I don't understand about WT identity is how it allows or helps you to renormalize a quantum field theory (es. QED). Not in details, just the basic ideas, if possible. Thanks in advice

Homework Statement Suppose that W is finite dimensional and T:V\rightarrow W. Prove that T is injective if and only if there exists S:W\rightarrow V such that ST is the identity map on V. Homework Equations The Attempt at a Solution First, suppose that T is injective and let...

I'm having trouble finding the identity of an operation. Could someone check my work? I'm trying to find the identity of x*y = x + 2y - xy In order to find the identity, I need to solve x*e = x for e \begin{align*} x*e &= x\\ x + 2e - xe &= x\\ 2e - xe &= 0\\ e(2-x) &= 0\\...

Homework Statement The series, 1 / (1 x 2) + 1 / (2 x 3) + 1 / (3 x 4) + ... + 1 / [n(n + 1)] + ... is not a geometric series. (A) Use the identity 1 / [k(k + 1)] = 1 / k - 1 / (k + 1) to find an expression for the nth partial sum Sn and (B) use it to find the sum of the...

Homework Statement If P is an orthogonal matrix with detP = -1, show that I+P has no inverse. (Hint: show that (P^t)(I+P)=(I+P)^t) P^t is P transposed. I is the identity matrix given by PP^t=I a^-1 means inverse a a, b, P and such letters, capital or otherwise, are all matrices, limit to...

Homework Statement Consider the function f:X \to Y. Suppose that A and B are subsets of X. Decide whether the following statements are necessarily true (I am including just the one I had trouble with): (a) if A\cap B = \emptyset , then f[A]\cap f[B] = \emptyset Homework Equations The...

Homework Statement cos\theta/1-tan\theta+sin\theta/1-cot\theta=sin\theta+cos\theta Homework Equations The Attempt at a Solution

I'm working on some trigonometry identity problems, and I'm stuck on this particular problem. This is how it is shown in the solution, but I cannot see how to get the highlighted part. Any help on how to get from #2 to #3 (the highlighted) is very much appreciated Jesper

How do you deduce that a1 - \sqrt{N} b1 = a2 - \sqrt{N}b2 to be a1=a2 and b1=b2?

Homework Statement Let z1 = a (cos (pi/4) + i sin (pi/4) ) and z2 = b (cos (pi/3) + i sin (pi/3)) Express (z1/z2)^3 in the form z = x + yi. ]2. Homework Equations [/b] The Attempt at a Solution a(cos (pi/4) + i sin (pi/4)) b (cos (pi/3) + i sin (pi/3)) I then multiplied...

Homework Statement Prove the Identity (show how the derivatives are the same): arcsin ((x - 1)/(x + 1)) = 2arctan (sqr(x) - pi/2) Homework Equations d/dx (arcsin x) = 1/ sqr(1 - x2) d/dx (arctan x) = 1/ (1 + x2) All my attempts have been messy and it may be because I didn't...

In electromagnetism J denotes the oriented charge-current density, J=d*F. Conservation of charge immediately follows. J=d2*F=0(identically). All exact forms are closed. We can identify scalar mass as the norm of the one-form, μ=(E/c2,-p/c). *μ is then spatial mass density. Like...

Hello, I'm working on some problems and I want to pose the following, though I am not completely sure it is correct. Can somebody point me to some sources on this? I have tried googling myself, but I only found differentiation identities with either just vectors and scalars on the on hand, or...

Can someone help me prove the identity \ u \times (\nabla \times u) = \nabla(u^2 /2) - (u.\nabla)u without having to write it out in components?

I'd like to see how many people can explain this identity: \frac{\partialx_{i}}{\partialx_{j}} = \delta_{ij}

Let's say I have a function that preservers ordering i.e if x<y then f(x)<f(y) for all x. Obviously it must follow that it's the identity function but how can I approach this?

Hi there, If A is unitary I understand that it obeys AA+=1 because A-1=A+. Why does A3=1? The explanation simply says that "A just permutes the basis vectors".. It then goes on to say that since A3=1, then eigenvalue a3=1 also, which are 1, ei.2pi.theta/3, and ei.4pi.theta/3. This...

SOLVED With the assumption f(x)\in L^1(\mathbb{R})\cap L^2(\mathbb{R}) (in a Lebesque sense) I'm trying to include a short proof of Plancherel's identity into my dissertation but am having trouble justifying the change of integration at the end of the following line...

Homework Statement http://img560.imageshack.us/img560/5384/unledkb.jpg The Attempt at a Solution For 21. I simply did div(\mathbf{F} + \mathbf{G}) = \vec{\nabla} \cdot (\mathbf{F} + \mathbf{G}) = \vec{\nabla} \cdot \mathbf{F} + \vec{\nabla} \cdot \mathbf{G} = div(\mathbf{F}) +...

So I've tried to wrap my head around this concept, and I just read the last two sections in this chapter in order to really get a proper mindset here. Despite reading, there are no examples in the book that pertain to these questions, nor is there anything saying what kind of problem it is and...

Hi I'm trying Q1 of this paper: http://www.maths.cam.ac.uk/postgrad/mathiii/pastpapers/2005/Paper60.pdf and have got to the bit where I need to show that \xi_{b;ca}=-R_{bca}{}^d \xi_d Now I know that R_{bca}{}^d \xi_d=R_{bcad} \xi^d = R_{adbc} \xi^d = \nabla_b \nabla_c \xi_a - \nabla_c...

Homework Statement The problem is finding the average value of momentum in an infinite potential well but the theory I understand, its the mathematical execution I'm having trouble with. Homework Equations The expectation value for the momentum is found using the conjugate formula...

I am so stuck on my revision and i really need someones help! I am using the definition of Fourier series as My lecturer has told us that if f is odd. Could someone please tell me how he has derived this because i can't understand how he's got to it, iv tried using trig identities and...

Homework Statement How does |sinx + cosx| = |sqrt(2)(x + (pi/4))| ? Homework Equations The Attempt at a Solution Some kind of co-function identity?

1-(sin^6x+cos^6x)=(3sin^2x)(cos^2x) I got this far: 1-(sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x)=(3sin^2x)(cos^2x) 1-(sin^4x-sin^2xcos^2x+cos^4x)=(3sin^2x)(cos^2x)

Homework Statement Suppose that the equation f(x,y,z)=0 can be solved for each of the three variables as a differentiable function of the other two. Prove that: (dx/dy)(dy/dz)(dz/dx)=-1 Homework Equations The Attempt at a Solution In the case of two variables where one is a...

Homework Statement Hi guys In my book they use the following identity e^{ - i\widehat Ht/\hbar } = e^{ - i\widehat Tt/\hbar } e^{ - i\widehat Vt/\hbar } + O(t^2 ) where H = T+V, and the last term means "terms of order t2 or higher". I can't quite see how they reach this identity. First...

Homework Statement I am trying to show that for a vector field Va which satisfies V_{a;b}+V_{b;a} that V_{a;b;c}=V_eR^e_{cba} using just the below identities. Homework Equations V_{a;b;c}-V_{a;c;b}=V_eR^e_{abc}(0) R^e_{abc}+R^e_{bca}+R^e_{cab}=0 (*) V_{a;b}+V_{b;a}=0 (**) The Attempt at a...

Using the fact that we can write the vector cross-product in the form: (A× B)i =ε ijk Aj Bk , where εijk is the Levi-Civita tensor show that: ∇×( fA) = f ∇× A− A×∇f , where A is a vector function and f a scalar function. Could you please be as descriptive as possible; as I'm not sure...

Any help please why the following algebraic identity is true \frac{k^2}{k^2-m^2} = 1 + \frac{m^2}{k^2-m^2} thanks

Sin \theta = -5/13, (3\pi / 2) < \theta < 2 \pi So I got cos \theta = - (sqrt 194) / 13 Is this the right answer?

we know that \Gamma (s)= \int_{0}^{\infty}dxe^{-x}x^{s-1} however every factor of the Riemann Zeta can be obtained also from a Mellin transform \int_{0}^{\infty}dxf(x)x^{s-1} =(1-p^{-s})^{-1} where f(x) is the distribution \sum_{n=0}^{\infty}x \delta (x-p^{-n}) is there any...

Homework Statement Reduce the equation \partial_\mu {*} F^{\mu \nu} = 0 into the following form of the Jacobi Identity: \partial_\lambda F_{\mu \nu} + \partial_\mu F_{\lambda \nu} + \partial_\nu F_{\lambda \mu} = 0 The Attempt at a Solution I can't figure out what the '*' is supposed to...

I saw this question in an abstract algebra text that I was reading. "Is it true that (w − x) − (y − z) = (w − y) − (x − z) is an identity for real numbers? Can you say why or why not?" I know that an identity element does not change the value of a real number. So 0 is the identity element...

Please teach me this: It seem to me the Ward-Takahashi is validated by the renormalization, if the theory can not be renormalized the proof of Ward identity is failed.In QED the Ward identity is validated by electrical charge renormalization. The Ward-Takahashi implies a current...

Homework Statement Homework Equations The Attempt at a Solution

Homework Statement How would I know if let's say Sec^2 = 5 / 4 Sec = +/- \sqrt{5/4} Sec = + / - \sqrt{5} / 2 Now how would I know if whether to put a negative sign or a positive sign before the answer? Because the textbook says Sec Theta < 0 therefor they added the negative sign...

i am trying to verify the following identity: 0 = ∂g_mn / ∂y^p + Γ ^s _pm g_sn + Γ ^r _pn g_mr where Γ is the christoffel symbol with ^ telling what is the upper index and _ telling what are the two lower indices. g_mn is the metric tensor with 2 lower indices and y^p is the component of y...

Homework Statement What conclusion can be drawn from the lines (x-x0)/a = (y-y0)/b = (z-z0)/c (x-x0)/A = (y-y0)/B = (z-z0)/C if aA + bB +cC = 0 Homework Equations The Attempt at a Solution I put everything in parametric form but that didn't do much for me. Is...

Homework Statement I am reading an explanation on a trig identity but I am not fully understanding it... Angle MOP = Theta Angle POP' = Right angle Angle AOP' = (Theta + Right angle) Take OP' = OP ( WHY must it be equal?) Angle MOP + P'OM' = 90 ( I understand this) Angle MOP = Angle...

I'm supposed to use the relationship A^{-1}=\int_0^\infty d \alpha e^{-\alpha A} to show that \frac{1}{A_1 A_2 \dots A_n}=(n-1)! \int_0^1 dx_1 \dots \int_0^1 dx_n \frac{\delta(1-x_1- \dots - x_n)}{(x_1A_1 + \dots + x_nA_n)^n} I decided that I should try and do this inductively. So far I...