Decomposition Definition and 414 Threads

Homework Statement Prove that the diagonal entries of R in the QR decomposition are non-zero. Homework Equations ui = qi + <ui, q1>q1 + <ui, q2>q2 + ... + <ui, qi-1>qi-1 => From the general equation for the Gram-Schmidt process. <ui, qi> => From the diagonal entries of QR. The...

I have 12000 x 12000 R(data class single) sparse matrix, and I want to find its eigen values and vectors, but I can't do it in matlab, it gives out of memory error by doing [V D] = eigs(R) and I am using 4GB RAM , online help suggested using ARPACK or ARPACK++ with C/C++. please any...

Homework Statement I want to do a singular value decomposition for the following matrix: M = \left\lceil 1 \ \ -1 \right\rceil \ \ \ \ \ \ \ \:\:\left\lfloor 1 \ \ -1 \right\rfloor Homework Equations M=U\Sigma V^{\ T} M^{\ T}M MM^{\ T} The Attempt at a Solution To...

Partial fraction decomposition for... [b]1. 3x-1 / x(x^2 +4) Homework Equations [b]3. A/x + Bx + C/ x^2 +4 after multiplying through by the denominator and my attempt at finding A,B,C i get this: 3x-1/x(x^2+4) = - one fourth / x + one fourth + 3/ x^2 +4. I don't feel...

Homework Statement Quick question, bros. Homework Equations Tell me if I'm right. The Attempt at a Solution A = U∑VT where ∑ contains on its diagonal the singular values of ATA U contains the corresponding eigenvectors for those singular values V...

I am currently trying to find how to derive the decomposition for two particles via the tensor notation, for instance for the product of two particles of spin 1/2 : \frac{1}{2} \otimes \frac{1}{2} = 1 \oplus 0 Giving the components of spin 1 and 0. So to do it, I write down the product...

Homework Statement [PLAIN]http://webwork2.math.utah.edu/webwork2_files/tmp/equations/60/0cff8a5107e21ae393dee5038fb6b31.png Homework Equations The Attempt at a Solution I've been attempting to use the general method of solving found at this website...

My notes are talking about this scalar vector tensor decopmosition business. Unfortunately, they are not online but they seem to follow this wikipedia article fairly closely: http://en.wikipedia.org/wiki/Scalar-vector-tensor_decomposition So our perturbed metric is of the form...

5x^2 + 8/x3 + x2 I got a 5x^2 + 8 = A/x^2 + B/x + 1 A(x+1) + B(x^2) (Ax+A) + (Bx^2) (Ax + Bx^2) + A 5x^2 + 8 = (A + B) x + (A)x^2 5x^2+x+8=(A+B) + (A) This is about as far as I can get but I think I made a mistake somewhere but I don't know where? Can someone help me?

Determine A and B in terms of a and b. ax + b divided by x^2− 9=A/x-3 + B=x+3 When i calculate it i get a+b/2 and a-b/2 but that's wrong. I need help with this one.

Hi When we decompose e.g. the vector potential A into a sum of plane waves, then is it correct to say that we are describing an arbitrary vector field A, since we have decomposed it into its Fourier (= plane wave) components?Niles.

Homework Statement The link http://www.york.ac.uk/depts/maths/data/ts/welcome.htm gives the average monthly temperature T in Fahrenheits for Dubuque, Iowa from 1964 to 1975. Let T = a0 + sum from i = 1 to k of ai cos(2*pi*i*m/12) + sum from i = 1 to k of bi sin(2*pi*i*m/12) where m is the...

Hello, I need to Bel-decompose the Riemann tensor built over SO(3,3). Does anyone have a decent reference? Funny how this topic is elusive. Is this in Wald? Thanks in advance. -drl

Homework Statement What is the Initial Rate of Decomposition for NO2. Where 2NO2-----> 2NO + O2 K=.54 Concentration at t=0 is .008 M This is a second order reaction.Homework Equations Rate=k[C]2The Attempt at a Solution Rate=.54[.008]2=.000035 (directed to give a two sig fig answer) This...

Homework Statement There is a particle in an infinite square well and the normalized wave function is divided into 3 parts. Psi = A between 0< x < L/3, B where L/3< x < 2L/3, and C from 2L/3 < x < L. I have to prove that the decomposition into psin yields a specific cn. Homework Equations...

Homework Statement Dinitrogen monoxide (nitrous oxide) N2O decomposes producing nitrogen and oxygen gases. The atomic masses are N: 14.0 and O: 16.0 The molar volume of an ideal gas at STP is 22.4 dm3/mol Homework Equations Calculate the total volume of produced gases at STP, when 8.8...

The equation i currently have is (-7s+52)/(s^2-8s+16) I need to convert it into a partial fraction decomposition to do a inverse Laplace Transform, but i seem to be stuck with the algebra of the what I am supposed to do. The equation I am supposed to use to set them is A/(s+a) +...

these are my mfiles for Lu decomposition with partial pivoting and substitution 1.LUdecomp.m function [x]=LUdecomp(a,b,n,tol,er,x) for i=1:n o(i)=0; s(i)=0; end er=0; decompose(a,n,tol,o,s,er) if er~=-1 substitute(a,o,n,b,x); end end 2.decompose.m function...

Homework Statement Using (\sigma^{\mu \nu})^{\beta}_{\alpha} (\sigma_{\mu \nu})^{\delta}_{\gamma} = \epsilon_{\alpha \gamma} \epsilon^{\beta \delta} + \delta^{\delta}_{\alpha} \delta^{\beta}_{\gamma} show that \Psi_{\alpha} X_{\beta} = \frac{1}{2} \epsilon_{\alpha \beta} (\Psi X) +...

Homework Statement Let H(r) = x^{2}yi + y^{2}zj + z^{2}xk. Find an irrotational function F(r) and a solenoidal function G(r) such that H(r) = F(r) + G(r) Homework Equations From Helmholtz's theorem, any vector field H can be expressed as: H = -\nabla\Psi + \nablaxA So then: F...

Homework Statement Let H(r) = x^{2}yi + y^{2}zj + z^{2}xk. Find an irrotational function F(r) and a solenoidal function G(r) such that H(r) = F(r) + G(r) Homework Equations From Helmholtz's theorem, any vector field H can be expressed as: H = -\nabla\Psi + \nablaxA So then: F =...

Hi... Can anyone one give me a good reference for the decomposition of perturbations into independent scalar, vector and tensor parts, with all the gory details?

Hello everybody, this is the first thread of mine. I try to recover the decomposition of the fundamental representation (the 7) of G2 into irreducible representations of A_2. It is given by 7 = 3 + [tex]\bar {3}[\tex] + 1 It maid be that I didn't understand the procedure, founded...

Homework Statement I've been looking at Paul Langacker's "Grand unified theories and proton decay" for a course on GUTs. I'm stuck with the 16 irrep of SO(10), particularly I don't understand how to prove the statement that the 16 decomposes as 5* + 10 + 1. I can see why it's useful physics...

Asymptotic analysis Hi, can someone please give me a highlight of asymptotic analysis and singular cauchy problems...how is asymptotic compared to convergence...to my understanding when you have a polynomial divided by a polynomial= solution + remainder...the solution is the asymptotic and the...

Homework Statement In the heat equation, we have $T(t,x)=sum of a_k(t)b_k(x)$. Now I want to find a formula for computing the initial coefficients $a_k(0)$ given the initial temperature distribution $f(x)$. Homework Equations We know that in a heat equation , $f(0)=0$, $f(1)=0$...

Homework Statement Calculate the empirical formula of each hydrate Homework Equations Mass of MnSO4 x XH2O... -Hydrate = 1.8g -Anhydrous salt = 1.59g -Water = .21g The Attempt at a Solution I thought you would set 1.8g MnSO4*XH2O((Molecular mass of MnSO4)/(Molecular mass of...

Homework Statement Let T be a linear transformation over V, a finite-dimensional complex inner product space (with inner product < , >). Suppose T has the singular value decomposition Tv = \sum_j^n s_j \left\langle v,e_j \right\rangle f_j where s_1, ... s_n are the singular values of T and...

I need to write a program utilizing LU decomposition of a matrix in Java without using any linear algebra libraries so I was wondering if anyone can give me some pseudo-code or a link or something. I know you're supposed to post your attempt, but I literally have no idea what I'm doing. This is...

For the following problem provide the "form" of the partial fraction decomposition for the given fractional expression. You do not have to solve the undetermined coefficients. 4. 2x^2 - 3x + 8 / x^3 + 9x I took an x out and it's no x(x^2+9) My answer is A/X + BX+C/x^2+9 5. x- 7 / x^4 - 16...

http://news.yahoo.com/s/yblog_upshot/20101012/bs_yblog_upshot/mcdonalds-happy-meal-resists-decomposition-for-six-months" . Who else here has observed several (or perhaps many, yech) food items which have "resisted decomposition" in the same way as Davies' Happy Meal Project? I find this...

Homework Statement Show that any linear operator \hat{O} can be decomposed as \hat{O}=\hat{O}'+i\hat{O}'', where \hat{O}' and \hat{O}'' are Hermitian operators. Homework Equations Operator is Hermitian if: T=T^{\dagger}The Attempt at a Solution I don't know where to start :\ Should I try...

Homework Statement Given matrix, A= (-1 0 2;2 -1 0) and B=(-3 4;2 1) Find SVD using matlab. Homework Equations The Attempt at a Solution matlab code for svd; [d,e,f]= svd(c) c= A*B (but i got an error in MATLAB when i tried this) thanks

Homework Statement Find a singular value decomposition of A. A^T= [7 0 5 1 0 5] Homework Equations A = U\SigmaV^T The Attempt at a Solution I started by doing A^T*A = [ 74 32 32 26] Then i went and found the two eigen values lambda1= 90 and lambda2= 10 and the...

Homework Statement y=[4 8 1]^T u_1 = [2/3 1/3 2/3]^T u_2=[-2/3 2/3 1/3]^T Part 1: Write y as the sum of a vector y hat in W and a vector z in W complement Part 2: Describe the geometric relationship between the plane W in R^3 and the vectors y hat and z from the part above...

[PLAIN]http://upload.wikimedia.org/wikipedia/en/7/7a/Friction.png I can decompose W to get Fn and -Fr. Fn = W cos(\theta) -Fr = W sin(\theta) I know I'm allowed to decompose forces like that but I'm a bit confused as to why. Cause |Fn| + |Fr| > |W| (for the angle in this picture). So...

We are a simple robotics group working in Antarctica. We have a small but nimble ROV that we launch through a hole we drill in the ice. We need to lift heavy objects off the sea floor. I want to use the decomposition of H2O2 to initiate a state change that creates the buoyancy to lift these...

Homework Statement Find the partial fraction decomposition 1. \frac{x^4}{(x-1)^3} 2. \frac{1}{a^2-x^2} Homework Equations The Attempt at a Solution 1. \frac{x^4}{(x-1)^3} \frac{x^4}{(x-1)^3}=\frac{a}{(x-1)}+\frac{b}{(x-1)^2}+\frac{c}{(x-1)^3} x^4=(x-1)^2+(x-1)b+c x^4=ax^2+(-2a+b)x+(a-b+c) I...

Homework Statement Write the Partial Fraction decomposition for: \frac{x}{16x^4-1} Homework Equations The Attempt at a Solution \frac{x}{16x^4-1} =\frac{x}{(2x-1)(2x+1)(4x^2+1)} =\frac{x}{(2x-1)(2x+1)(4x^2+1)}=\frac{a}{(2x-1)}+\frac{b}{(2x+1)}+\frac{cx+d}{4x^2+1}...

Homework Statement Find the Partial Fraction Decomposition. \frac{4x^2+2x-1}{x^2(x+1)} Homework Equations The Attempt at a Solution \frac{4x^2+2x-1}{x^2(x+1)}=\frac{a}{x}+\frac{b}{x^2}+\frac{c}{(x+1)} 4x^2+2x-1=x^2(x+1)a+x(x+1)b+x^2(x)c So i can solve for c by plugging in...

Homework Statement \int 1/(x^{2}+4x+5)^{2} Homework Equations I am using partial fraction decomposition The Attempt at a Solution 1/(x^{2}+4x+5)^{2} = Ax+b/(X^2+4x+5) + Cx+D/(x^2+4x+5)^2 1 = (Ax+b)(X^2+4x+5) + Cx+D When i multiply through to find the values for A and b...

Hello all, I have a small problem that I would appreciate some assistance with. I'm working with the Lie group \mathfrak U(N) of unitary matrices and I have an element P \in \mathfrak U(N) . Furthermore, I have a set \left\{ H_1, \ldots, H_d \right\} that generate the Lie algebra...

Does anyone know of a good discussion of the compatibility (or otherwise) of Weinberg's 'cluster decomposition' principle with the fact that entangled states yield distant but correlated measurements?

Linear Algebra - Cyclic Decomposition, Rational Canonical Form Homework Statement I am given a 5x5 real matrix A, and I am looking for an invertible matrix P so that P^{-1}AP is in rational form. Homework Equations The Attempt at a Solution I calculated the characteristic...

Homework Statement \frac{2x + 2}{x^2 - 2x + 1}dxHomework Equations The Attempt at a Solution I factorized the denominator and got \frac{2x + 2}{(x - 1)^2} and I took a look at the solutions manual to see how they handled this but then I see this \frac{2x + 2}{(x - 1)^2} = \frac{A}{(x - 1)} +...

Homework Statement Write the partial fraction decomposition of the rational expression. Check your result algebraically. (x2 – 7x + 16)/[(x + 2)(x2 – 4x + 5)] The Attempt at a Solution [A/(x+2)] + [(Bx+C)/(x2-4x+5)] x2-7x+16= A(X2-4x+5)+(Bx+C)(x+2)...

First i calculated the eigenvalues: I got (i-\lambda)(-i-\lambda)+1, so \lambda_{1,2}=+-\sqrt{2}i Is it correct to go on on like this: \lambda_{1}a+b=\sqrt{\lambda_{1}} \lambda_{2}a+b=\sqrt{\lambda_{2}} After calculating a and b, we plug it into f(x) = ax+b --> f(A^{*}A)=a(A^{*}A)+bI Then...

Im attempting a problem in relativistic optics that's asking me to write k_x, k_y and k_z in terms of lambda, c, and theta (theta being the angle between a source and an observer, at rest relative to each other). Lamda is the wavelength in this reference frame. I started off using trigonometry...

Homework Statement A sample consisting of 1.0 mol of calcium carbonate CaCO3(s) was heated to 800°C, when it decomposed (CaCO3 → CaO + CO2). The heating was carried out in a container fitted with a piston which was initially resting on the solid. Calculate the work done during complete...

Homework Statement Decompose the rational expression into a sum of partial fractions: (x+1)/(3(x-2)2) I am familiar with the method of decomposing fractions into a sum of partials fractions (solving for A, B, C, etc.). What is confusing me is the coefficient 3 in the denominator. Do I...