Decomposition Definition and 386 Threads

Homework Statement Find the decomposition of the standard two-dimensional rotation representation of the cyclic group Cn by rotations into irreducible representations The Attempt at a Solution Ok i did this directly, finding complementary 1-dimensional G-invariant subspaces. but...

I am just coming back to math after a, oh 30 year or so, vacation. In the class I'm taking, we are studying Partial Fraction Decomposition ( Px/Qx:Qx). It doesn't entirely make sense to me, tho like a monkey typing the great American novel, I can solve them given enough time. I am just having...

I'm trying to find a divergenceless vector field based on its curl, and discovered that I could use a http://en.wikipedia.org/wiki/Helmholtz_decomposition" , and the article I found on this didn't make much sense to me. First, can someone confirm that the dimension referred to in the...

I'm trying to find a divergenceless vector field based on its curl, and discovered that I could use a http://en.wikipedia.org/wiki/Helmholtz_decomposition" , and the article I found on this didn't make much sense to me. First, can someone confirm that the dimension referred to in the...

Wikipedia defines the Shur decomposition of matrix A as A = Q U Q^{-1} where Q is unitary and U is upper triangular. http://en.wikipedia.org/wiki/Schur_decomposition Mathworld defines the Shur decomposition of matrix A as Q^H A Q = T, where Q is unitary and T is upper...

Has there been any real scientific testing to determine the ratio of aging or decomposition of space junk above our atmosphere compared to atmospheric aging? I ask this because if space junk is going to be "out there" for millions of years as is, why would we even consider adding more in the...

Homework Statement Let A be a real or complex nxn matrix with Jordan decomposition A = X \Lambda X^{-1} where \Lambda is a diagonal matrix with diagonal elements \lambda_1,..., \lambda_n. Show that for any polynomial p(x): p(A)=Xp(\Lambda)X^{-1} p(\Lambda) should really be the matrix with...

Hello, I studying General Relativity at University of Chicago and I am looking for information regarding "Fourier-Harmonic Mode Decomposition" or mode decomposition in general and "Retarded Greens Functions" and retarded fields in general. Does anyone have advice about where is a good...

Homework Statement Let A be a complex or real square matrix. Suppose we have a Jordan decomposition A = XJX-1, where X is non-singular and J is upper bidiagonal. Show how you can obtain a Schur Decomposition from a Jordan Decomposition. Homework Equations Schur Decomposition: A = QTQ*...

Homework Statement Find the partial fraction decomposition of : \frac{x^2}{(1-x^4)^2} The Attempt at a Solution \frac{x^2}{(1-x^4)^2}=\frac{A}{(1-x^4)}+\frac {B}{(1-x^4)^2} =A(1-x^4)+B when x=1 1=A(1-1^4)+B Hence B=1 and A=0 \frac{x^2}{(1-x^4)^2}=\frac{0}{(1-x^4)}+ \frac{1}{(1-x^4)^2}...

Hi, I have a practical assessment tomorrow which deals with the Thermal Decomposition of a metal Carbonate. Is it possible to write Ionic Equations for the reaction? Ionic solids and solutions are involved, but the reactions seem to be Double Decomposition, especially the test for CO2 Also...

I'm supposed to prove this step as part of my proof for existence of Cholesky Decomposition. I can see how to use it in my proof, but I can't seem to be able to prove this lemma: For any positive (nxn) matrix A and any non-singular (nxn) matrix X, prove that B=X^{\dagger}A X is...

Homework Statement Let A be a real mxn matrix, m>=n, with singular values \sigmaj.Show that the singular values of (\stackrel{I_{n}}{A}) are equal to \sqrt{1+\sigma_j^2}. Homework Equations The Attempt at a Solution I know that an SVD for A is A = U(\stackrel{\Sigma}{0})v^T and...

First Order Decomposition -> % of compound. Please help! Homework Statement In a first order decomposition, the constant is 0.00313 sec-1. What percentage of the compound has decomposed after 7.17 minutes? Homework Equations rate = ln[A]o - ln[A]t = kt The Attempt at a Solution I...

HELP! on Partial Fraction Decomposition Problem! - Heavy Side Technique I am doing a partial fraction decomposition problem for my calc 2 class. We use the Heavy Side Technique, but I will take help either way! \frac{2x-1}{x(x^2+1)^2} Thank you!

Say X is a CW-complex. Then for any n, the n-skeleton X^n of X is obtained from the (n-1)-skeleton X^(n-1) by gluing some n-cells on X^(n-1) along their boundary. From what I read, it seems that the way to obtain X^n from X^(n-1) in this way is not unique. Is this non-uniqueness superfluous...

Given random variables X and Y, which are not independent, is it always possible to find a random variable W which is independent from X, such that Y = f(X,W), for some function f? Example: let the joint distribution of X and Y be Y 0 1 X+------- 0|1/3 1/6 1|1/6 1/3 Then if we...

Homework Statement I need to find a Jordan decomposition for: \[ \left( \begin{array}{cccc} 2 & 0 & 1 & 2 \\ -1 & 3 & 0 & -1 \\ 2 & -2 & 4 & 6 \\ -1 & 1 & -1 & -1 \end{array} \right)\] Homework Equations The Attempt at a Solution I found the eigenvalues: 2 (m=4). I also found the eigenvectors...

[b]1. Let T be the linear operator on R^n that has the given matrix A relative to the standard basis. Find the spectral decomposition of T. A= 7, 3, 3, 2 0, 1, 2,-4 -8,-4,-5,0 2, 1, 2, 3 [b]3. eigen values are 1 (mulitplicity 1), -1 (mult. 1), 3 (mult. 2). And associated eigen...

I am looking for a mechanism to find a decomposition of symmetric groups. For finitely generated abelian group G, there is a mechanism to decompose G such that G is isomorphic to a direct sum of cyclic groups. For symmetric groups, it seems a bit complex for me to find it. For example...

Homework Statement let a=(b_1,...,b_n) n-cycle in the permutation group S_n . prove that the cycle decomposition of a^k consist of gcd(n,k) cycles of n/gcd(n,k) size. The Attempt at a Solution I know that a^k(b_i)=b_{i+k (mod n)} how can it help me ?

Homework Statement \frac{4x^{4}-8x^{3}+5x^{2}-2x-1}{2x^{2}-3x-2} Homework Equations The Attempt at a Solution I started of by breaking the bottom part down into (2x+1)(x-2) which then allowed me to set... \frac{A}{(2x+1)}+\frac{B}{(x-2)} The problem is from here I tried...

Homework Statement http://img296.imageshack.us/img296/6584/93872041bz2.png Homework Equations http://img208.imageshack.us/img208/2062/55585340nj2.png The Attempt at a Solution I think the key to the solution is the matrix A being non-singular but I can't see how.

In finite dimensions, a matrix can be decomposed into the sum of rank-1 matrices. This got me thinking - in what situations can a bounded linear operator mapping between infinite dimensional spaces be written as an (infinite) sum of rank-1 operators? eg, let A be a bounded linear operator...

What I'm wondering is: Q and R in the QR decomposition of A are the same Q and R in the RQ decomposition of which matrix? I found some MATLAB code which will get RQ from QR, but I don't understand how you would do those operations FIRST, then find the QR decomposition. ReverseRows = [0...

How can you prove that matrix X with rank n can be written as the sum of matrices Y and Z where Y has rank n-1 and Z has rank of 1. Thanks!

I'm trying to solve this integral but I'm not sure if I'm on the right track. My question is: can this integral be solved by partial fractions decomposition? I solved the problem that way but I'm not sure if it is the right answer. thanks! ∫1-x+2x^2-x^3 ÷ x(x^2+1)^2

Homework Statement 0 0 1 1 0 0 0 1 0 decompose this matrix using LU decomposition. Homework Equations The Attempt at a Solution I took this matrix and augmented it with a zero (3 by 3) matrix. Then I performed the same row operations on both...the row operations with the...

Can anyone explain to me why the 3-rep of SU(3) gives 3\otimes 3 = \overline{3}\oplus 6 whereas for the 5 of SU(5) 5\otimes 5 = 10\oplus 15? I thought the general pattern was N \otimes N = \overline{\frac{1}{2}N(N-1)}\oplus \frac{1}{2}N(N+1) but this second example seems to...

(Keep in mind, I made this off the top of my head, so if something cancels easy, ignore it) Let's say I had this expression: f(x,y)=\frac{y^2-xy+1}{(x+y)(x-y)} I want to decompose this to: \frac{A}{x+y} + \frac{B}{x-y} So i begin the process: y^2-xy+1=A(x-y) + B(x+y) y^2-xy+1=x(A+B) +...

I am having trouble finding information about decomposing a complex symmetric positive definite matrix. I was wondering if the cholesky decomposition would change to accommodate complex numbers. I understand that multiplying, dividing, and taking the square root of complex numbers is not the...

I am having trouble finding information about decomposing a complex symmetric positive definite matrix. I was wondering if the cholesky decomposition would change to accommodate complex numbers. I understand that multiplying, dividing, and taking the square root of complex numbers is not the...

Problem: Find the integral of 2dx/(2x-3) using partial fraction decomposition Attempt: A/(2x-3) Compare coefficients A = 2 2 \int (1/(2x-3)) = 2ln(2x-3) This is wrong. Can someone please tell me what I'm doing wrong?

I did some problems from the example and the questions at end of chapter. I got all of them right except this one. Problem Statement: Consider the matrix [3 0; 0 -2]. Find its singular value decompositions Problem Solution Goal is to find A = U*S*V as below Step1: Find AA', A'A...

Homework Statement I am just trying to do partial fraction decomposition on an equation. I'm not too good with it, as far as knowing if I need just A or Ax+B, etc. [e^(-2s) / (s^2+1)(s-1)(s+1)^2] Homework Equations The Attempt at a Solution I'm not quite sure how to work with the...

Hi, I've been doing some work with the NS equations. I've read a few papers by fellow undergrads that imply a relationship between the helmholtz-hodge decomposition and the pressure equation. As far as I can see, they're both separate ways of resolving the problem of keeping the flow...

Hi all: I have a covariance matrix which is like: 0.00166713 -0.00060678 4.60534e-05 -0.00060678 0.00178576 -0.000244526 4.60534e-05 -0.000244526 0.000772057 And then I want to eigen decompose the matrix to obtain the eigenvector matrix. I tried several methods, one is to use the...

Homework Statement Calculate \sum_{n=2}^{\infty}\frac{1}{n^{2}-1} with the "standard" method and with the method of the partial fraction decomposition of the cosine. Homework Equations \pi\cot\pi z=\frac{1}{z}+\sum_{k=1}^{\infty}\frac{2z}{z^{2}-k^{2}} The Attempt at a...

Hey guys, Homework Statement Basically the question is to explain the meaning of a SHD of an image, specifically the image of the WMAP data of the CMB. Now i understand decomposition when it comes to functions but I am not sure how to extend that to images. Is it simply that you are...

I'm doing some work with vectors, and essentially, I have two vectors: a large vector and a unit vector pointing in a different direction. I would like to decompose the large vector into the components that are in the direction of and perpendicular to the unit vector. This is in three...

hi... I´m attending a course of advanced classical mechanics. I´m working on statistical mechanics, so I´m not so familiar with some things on the course. I must solve the follwing problem for homework: [FONT="Arial"]show that every galilean transformation g on the (galilean space, using...

Hey folks, I'm trying to show that \sum_{m,n=-\infty}^\infty '(n^2+a^2m^2)^{-s}=\sum_{n=-\infty}^\infty 'n^{-2s}+\sum_{m=-\infty}^\infty'\sum_{n=-\infty}^\infty(n^2+a^2m^2)^{-s}. The prime means that we don't include the m=n=0 term. Has anyone seen this relation? Is it standard? Thanks!

\frac{7}{3s^{2}(3s+1)} Can this be decomposed, and how?

Homework Statement Lab Experiment: I added 5g of Cu2CO3(OH)2 in a bunsen burner and the resultant was a black product weighing 3.327g, representing a mass ratio of 0.67/1.0 Homework Equations The question is whether the remaining black compound is anhydrous copper carbonate...

Homework Statement Go here: http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/1999s.pdf You do not need to read the problem. In solution two for 1999 A3, I can do the partial fraction decomposition but I get something different from that... I am wondering whether that comes from...

Hey guys, Couple of questions here id like some help with. Firstly an unnamed theorem in my textbook that says: suppose s and t are distinct eigenvalues for a 2x2 matrix A, then (A-sI)(A-tI) = 0 The proof goes something like this. We know there is an eigenvector u for the value s such that...

2H2O2---> 2H2O+O2 In the decomposition equation above, how many grams of oxygen is made when 15.0 grams of H2O2 decomposes?

If you have a function f(x), you can decompose it as an infinite sum of sine waves of the form sin(nx) and cos(nx) for increasing n. If you have a function g(theta,phi), you can decompose it into spherical harmonics; for each order l you have 2l+1 spherical harmonics. Is there anything special...

Gordon decomposition an "right" current I've got a question about the Dirac equation and the Gordon decomposition of the dirac current. The Gordon decomposition is \bar \psi \gamma^\mu \psi = - \frac{1}{m}\Im (\bar \psi \partial^\mu \psi) - \frac{1}{2m}\partial_\mu ( \bar \psi...

Let A= [ 1 -2 -1 2] [-1 0 3 -2 ] [ 3 -4 -5 6] (sorry, can't line up the columns) I think I've done a) and b) correctly, I don't really understand c), d) and e) a) Find RowA and Nul A RowA={( 1, -2, -1, 2), (0, 1, -1, 0)} Nul A= {(3, 1, 1, 0), (-2, 0, 0, 1)} b) If...