Eigenvalues Definition and 853 Threads

I'm trying to create an algorithm in MATLAB, but I have a problem. According to theory, if G is a positive definite matrix, then it's eigenvalues are positive real numbers. I'm using function EIG() to calculate the eigenvalues and eigenvectors of matrices, but I almost always take and negative...

"sum" over Eigenvalues... Is there any mathematical meaning or it's used in Calculus or other 2branch" of mathematics de expression: \sum_{n} e^{-u\lambda (n) } where every "lambda" is just an Eigenvalue of a linear operator: L[y]=-\lambda _{n} y We Physicist know it as the...

This is a very simple question, but I can't seem to get it right, there's probably something silly that I'm missing here. Here's the question: I have A system in the l=1 state, and I have L_z|\ket{lm} = \hbar m\ket{lm}and L^2 \ket{lm} = \hbar^2 l(l+1)\ket{lm} I need to find the eigenvalues...

:rolleyes: :cool: I have a question..yesterday at Wikipedia i heard about the "Hermite Polynomials2 as Eigenfunctions of Fourier (complex?) transform with Eigenvalues i^{n} and i^{-n}...could someone explain what it refers with that?...when it says "Eigenfunctions-values" it refers to the...

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

Why do they have to purely imaginary? I got a proof that looks like Ax=ax where a = eigenvalue therefore Ax.x = ax.x = a|x|^2 Ax.x = x.(A^t)x where A^t = transpose = -A x.(-A)x = -b|x|^2 therefore a=-b, where b = conjugate of a Now is this as far as i need to go?

Please help me I am hopelessly lost and don't even know where to start! I guess they're right when they said girls suck at math! It's not fair! :redface: Let A be an nxn matrix with only real eigenvalues. Prove that there is an orthogonal matrix Q such that (Q^T)AQ is upper triangular with...

matrix A = \left(\begin{array}{ccc}3&0&0 \\ 0&3&0 \\3&0&0 \end{array}\right) has two real eigenvalues lambda_1=3 of multiplicity 2, and lambda_2=0 of multiplicity 1. find the eigenspace. A = \left(\begin{array}{ccc}3-3 &0&0 \\ 0&3-3&0 \\3&0&0-3 \end{array}\right) A =...

I need a bit of help with these boundary value problems. I'm trying to find their eigenvalues and eigenfunctions and although I pretty much know how to do it, I want to exactly WHY I'm doing each step. I attached part of my work, and on it I have a little question next to the steps I need...

If I have two positive definite Hermitian NxN matrices A and B, if I adiabatically change the components of A to B (constraining any intermediate matrices to be Hermitian as well, but not necessarily positive definite) while \"following\" the eigenvalues ... will the mapping of the eigenvalues...

"Suppose V is a (real or complex) inner product space, and that T:V\rightarrow V is self adjoint. Suppose that there is a vector v with ||v||=1, a scalar \lambda\in F and a real \epsilon >0 such that ||T(v)-\lambda v||<\epsilon. Show that T has an eigenvalue \lambda ' such that |\lambda...

In my textbook recently I stumbled across the following: Give a general description of those matrices which have two real eigenvalues equal in 'size' but opposite in sign? Could anyone explain this again very simply :-)

Hey! Does someone know of some resources which describe how to code a function which calculates the eigenvalues of a matrix? This could be either resources on the net or a book. If you know of a good book which teaches about programming and mathematics together in general I'd be happy to know...

Show that every eigenvalue of A is zero iff A is nilpotent (A^k = 0 for k>=1) i m having trouble with going from right to left (left to right i got) we know that det A = product of the eignevalues = 0 when we solve for the eigenvalues and put hte characteristic polynomial = 0 then det...

I'm asked to find the eigenvalues and eigenvectors of an nxn matrix. Up until now I thought eigenvectors and eigenvalues are something that's related to linear transformations. The said matrix is not one of any linear transformation. What do I do?

is there any trick for finding the eigenvalues and vectors for this kind of matrix? \left( \begin{array}{ccccc} 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & \sqrt{\frac{3}{2} & 0 & 0 \\ 0 & \sqrt{\frac{3}{2} & 0 & \sqrt{\frac{3}{2} & 0 \\ 0 & 0 & \sqrt{\frac{3}{2} & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \\ \end{array}...

I need help with an integral eigenvalue equation...I am lost on how to handle this: \int_{-\infty}^{\infty} dy K(x,y) \psi_n(y) = \lambda_n \psi_n(x) The kernel, K(x,y) is a 2D, correlated Gaussian. I have read that for this case an analytic solution exist for the eigenvalues, \lambda_n...

I need to find the eigenvalues and eigenvectors of a matrix of the form \left ( \begin{array}{cc} X_1 & X_2 \\ X_2 & X_1 \end{array} \right ) where the X_i's are themselves M \times M matrices of the form X_i = x_i \left ( \begin{array}{cccc} 1 & 1 & \cdots & 1 \\ 1 & 1 & \cdots &...

if you have a differential equation of the form x' = Ax where A is the coefficient matrix, and you get a triple eigenvalue with a defect of 1. (meaning you get v1 and v2 as the associated eigenvector). How do you get v3 and how do you set up the solutions? I tried finding v3 such that...

Let A be an nxn mx with n distinct eigenvalues and let B be an nxn mx with AB=BA. if X is an eigenvector of A, show that BX is zero or is an eigenvector of A with the same eigenvalue. Conclude that X is also an eigenvector of B. I could show BX is zero or is an eigenvector of A with the...

I've got a homework problem that I am needing to do; however, I am not sure really what the question is asking. Obviously since I don't know what is being asked, I don't know where to begin. I was hoping for some insight. Question: Show that matrix A = {cos (theta) sin (theta), -sin...

I have a question that deals with all three of the terms in the title. I'm not really even sure where to begin on this. I was hoping someone could help. Question: An n x n matrix A is said to be idempotent if A^2 = A. Show that if λ is an eigenvalue of an independent matrix, then λ must...

I have two excercises which have been causing me to tear my hair off for some time now. (a) the power method to find largest eigenvalue of A is defined as x(k+1) = Ax(k) (b) the inverse power method is to solve Ax(k+1) = x(k) to find smallest eigenvalue of A (c) the smallest/largest...

Hi, How can you infer from these equations, a = b_{max}(b_{max}+\hbar) \quad \text{and} \quad a = b_{min}(b_{min}-\hbar), that b_{max} = -b_{min}? It is used in the derivation of the angular momentum eigenvalues...

I have the tridiagonal matrix (which comes from the backward Euler scheme) A = [ 1+2M - M 0 ... ] [ -M 1+2M 0 ... ] [ ... ] [ -M 1+2M ] I am given that the...

Hi, I'm wondering if there is some kind of shortcut for finding the eigenvalues and eigenvectors of the following matrix. C = \left[ {\begin{array}{*{20}c} {0.8} & {0.3} \\ {0.3} & {0.7} \\ \end{array}} \right] Solving the equation \det \left( {C - \lambda I} \right) = 0, I...

confused on finding Eigenvalues and Eigenvectors! hello everyone, i can't understand this example, how did they find the Eigen value of 3?! Aslo an Eigen vector of 1 1? http://img438.imageshack.us/img438/1466/lastscan1oc.jpg thanks.

Hi I'm stuck on the following question and I have little idea as to how to proceed. Note: I only know how to calculate eigenvalues of a matrix, I don't many applications of them(apart from finding powers of matrices). Also, I will denote the inner product by <a,b> rather than with circular...

I'm experiencing difficulties trying to find the eigenvalues of the follow matrix. The hint is to use an elementary row operation to simplify C - \lambda I but I can't think of a suitable one to use or figure out whether a single row operation will actually make the calculations simpler. C...

hi, i have trouble understanding these two terms. can anyone explain to me eigenvalues and eigenvectors in laymen terms? Thks in advance! :smile:

howdy all, i need some answers if possible suppose i have a particle mass m, confinded in a 3d box sides L,2L,2L what would be the energy eigenvalues of this particle i presumed it to be: hcross*w*A where hcross is h/2*pi w is omega and A is the...

This is probably a straight forward question, but can someone show me how to solve this problem: \frac {d^2} {d \phi^2} f(\phi) = q f(\phi) I need to solve for f, and the solution indicates the answer is: f_{\substack{+\\-}} (\phi) = A e^{\substack{+\\-} \sqrt{q} \phi} I know...

1). suppose that y1, y2, y3 are the eigenvalues of a 3 by 3 matrix A, and suppose that u1, u2,u3 are corresponding eigenvectors. Prove that if { u1, u2, u3 } is a linearly independent set and if p(t) is the characteristic polynomial for A, then p(A) is the zero matrix. I thought...

i'm reading and doing some work in introduction to linear algebra fifth edition, and i came across some problems that i had no clue. 1. An (n x n) matrix A is a skew symmetric (A(transposed) = -A). Argue that an (n x n) skew-symmetrix matrix is singular when n is an odd integer. 2. Prove...

This thread, https://www.physicsforums.com/showthread.php?t=74810, was orignally posted here in the QM forum, but it was moved to the homework section, which is reasonable. But nobody there knows quantum mechanics. I guess the OP gave up on it, but I'm curious how to do the problem now. So if...

Hi. I have this problem which i am stuck at: Consider a one-dimensional Hamilton operator of the form H = \frac{P^2}{2M} - |v\rangle V \langle v| where the potential strength V is a postive constant and |v \rangle\langle v| is a normalised projector, \langle v|v \rangle = 1 ...

If L^2 |f> = k^2 |f>, where L is a linear operator, |f> is a function, and k is a scalar, does that mean that L|f> = +/- k |f>? How would you prove this?

In a recent thread https://www.physicsforums.com/showthread.php?t=67366 matt and cronxeh seemed to imply that we should all know that the product of the eigenvalues of a matrix equals its determinant. I don't remember hearing that very useful fact when I took linear algebra (except in the...

Hi, I need help on these questions for an assignment. I've been working on them for a couple of days and not getting anywhere. Any help would be appreciated... 1) A certain 4X4 real matrix is known to have these properties: 1. Two fo the eigenvalues of A are 3 and 2 2. the number 3 is an...

I having trouble finding the eigenvalues and eigenfunctions for the operator \hat{Q} = \frac{d^2}{d\phi^2}, where \phi is the azimuthal angle. The eigenfunctions are periodical, f(\phi) = f(\phi + 2\pi), which I think should put some restrictions on the eigenvalues. I think...

How can i find the eigen value(s) of A - (alpha)I where A is an arbitrary matrix ?

Hello: -was solving for the eigenvalues of a matrix. Obtained: \lambda = 1 \pm 2i -substituted back into matrix to try and solve for the eigenvectors: \left(\begin{array}{cc}2-2i & -2\\4 & -2-2i\end{array}\right) \left(\begin{array}{cc}x_1 \\ x_2 \end{array}\right) = \mathbf{0}...

let A be a diagonalizable matrix with eignvalues = x1, x2, ..., xn the characteristic polynomial of A is p (x) = a1 (x)^n + a2 (x)^n-1 + ...+an+1 show that inverse A = q (A) for some polynomial q of degree less than n

I'm having trouble getting started on this problem... I just really don't understand what to do. Solve X'+2X'+(\lambda-\alpha)X=0, 0<x<1 X(0)=0 X'(1)=0 a. Is \lambda=1+\alpha an eigenvalue? What is the corresponding eigenfunction? b. Find the equation that the other eigenvalues...

I'm trying to find the basis for a particular matrix and I get a 3 eigenvalues with two of them being identical to each other. What do I do to find the basis for the repeated eigenvalue? Will it have the same basis as the original number? Thanks!

I'm reading an introductionary text on quantum physics and am stumbling a bit with the terms used. The text discusses a finite potential box (one dimension, time independent). It calculates the conditions for the solutions of the wave functions, which I can follow perfectly. At that point...

let's say.. there is a particle, with mass m, in a 2-dimensions x-y plane. in a region 0 < x < 3L ; 0 < y < 2L how to calculate the energy eigenvalues and eigenfunctions of the particle? thx :smile: and.. 2nd question.. there is a particle of kinetic energy E is incident from...

Who knows the formula to calculate the eigenvalues of total angular momentum between two different states? In particular, what is the matrix element of <S, L, J, M_J | J^2 | S', L', J', M'_J> ? Thank's...

spanning sets, eigenvalues, eigenvectors etc... can anyone please explain to me what a spanning set is? I've been having some difficulty with this for a long time and my final exam is almost here. also, what are eigenvalues and eigenvectors? i know how to calculate them but i don't understand...

Find the eigenvalues and eigenvectors of the general real symmetric 2 x 2 matrix A= a b b c The two eigenvalues that I got are a-b and c-b. I got these values from this: (a-eigenvalue)(c-eigenvalue)-b^2=0 (a-eigenvalue)(c-eigenvalue) = b^2 (a-eigenvalue)= b = a-b...