Eigenvalues Definition and 820 Threads

Hi there. First of all, sorry for my bad english. I ´m trying to solve next exercise, from Vibrations and Waves in Continuos Mechanical Systems (Hagedorn, DasGupta): Determine the eigenfrequencies and mode-shapes of transverse vibration of a taut string with fixed ends and a discrete mass in the...

Hi to all. Say that you have an eigenvalue problem of a Hermitian matrix ##A## and want (for many reasons) to calculate the eigenvalues and eigenstates for many cases where only the diagonal elements are changed in each case. Say the common eigenvalue problem is ##Ax=λx##. The ##A## matrix is...

Homework Statement So just curious about a specific problem that I am worries about running into on my test tomorrow. When trying to find eigen vectors with the eigen values what is there is a discrepancy between the two systems obtained after doing the matrix arithmetic? such as after using...

Effie has correctly found that the eigenvalues of $\displaystyle \begin{align*} A = \left[ \begin{matrix} \phantom{-}3 & \phantom{-}2 \\ -3 & -4 \end{matrix} \right] \end{align*}$ are $\displaystyle \begin{align*} \lambda_1 = -3 \end{align*}$ and $\displaystyle \begin{align*} \lambda_2 = 2...

Homework Statement Due to the radial symmetry of the Hamiltonian, H=-(ħ2/2m)∇2+k(x^2+y^2+z^2)/2 it should be possible to express stationary solutions to schrodinger's wave equation as eigenfunctions of the angular momentum operators L2 and Lz, where...

Suppose ##V## is a complex vector space of dimension ##n## and ##T## an operator in it. Furthermore, suppose ##v\in V##. Then I form a list of vectors in ##V##, ##(v,Tv,T^2v,\ldots,T^mv)## where ##m>n##. Due to the last inequality, the vectors in that list must be linearly dependent. This...

So, after time-independent 1D Schrodinger equation is solved, this is obtained E = n2π2ħ2/(2mL2) This means that the mass of the 'particle' is inversely related to the energy eigenvalue. Does this mean that the actual energy of the particle is inversely related to its mass? Isn't this counter...

Homework Statement I have the following matrix: 0 0 0 1 1 0 0 0 = A 0 1 0 0 0 0 1 0 and the vector v = (1,0,0,0) If I perform Av, this gives: Av=(0,1,0,0) And If I keep multiplying the result by A like A*A*(Av), the outcome will be something like j= (0,0,1,0) k=(0,0,0,1) l=(1,0,0,0) The...

And back again with a strange/odd layman question: Actually, this remark of Jilang is a perfect illustration of what I am wondering about: It seems as if realism and locality are behaving like two eigenstates in a space of interpretations of QM. Most people seem to suggest that you must have...

Mark44 submitted a new PF Insights post What Are Eigenvectors and Eigenvalues? Continue reading the Original PF Insights Post.

Homework Statement Explain in your own words why the product of eigenvalues of any diagonalisable N × N matrix A must equal the determinant of A. Homework Equations MT=M-1 The Attempt at a Solution So what I do know: the determinant measures the change in area of the unit square under the...

Hello all, I have a matrix A and I am looking for it's eigenvalues. No matter what I do, I find that the eigenvalues are 0, 1 and (k+1), while the answer of both the book and Maple is 0 and (k+2). I tried two different technical approaches, both led to the same place. The matrix is...

Homework Statement X= 1st row: (0, 1, 0, 0), 2nd row: (1, 0, 0, 0), 3rd row: (0, 0, 0, 1-i), 4th row: (0, 0, 1+i, 0) Find the eigenvalues and eigenvectors of the matrix X. Homework Equations |X-λI|=0 (characteristic equation) (λ is the eigenvalues, I is the identity matrix) (X-λI)V=0 (V is the...

Homework Statement Given the linear transformation l : R 2 → R 2 defined below, find characteristic equation, real eigenvalues and corresponding eigenvectors. a) l(x, y) = (x + 5y, 2x + 4y) Homework Equations characteristic equation = det (A-λI) = 0 The Attempt at a Solution l(x, y) = (x +...

Homework Statement Homework Equations $$E_n^{(2)}=\sum_{k\neq n}\frac{|H_{kn}'|^2}{E_n^{(0)}-e_k^{(0)}}$$ The Attempt at a Solution Not sure where to start here. The question doesn't give any information about the unperturbed Hamiltonian. Some guidance on the direction would be great...

Hello all I have a theoretical question. I know how to find the eigenvalues and eigenvectors of a matrix A. What I am not sure about, is what it all means and why do we need it for. I did some reading, and saw something about stretching vector, if I not mistaken, if I have a vector v, and I...

I've been playing around with the Carminati-McLenaghan invariants https://en.wikipedia.org/wiki/Carminati–McLenaghan_invariants , which are a set of curvature scalars based on the Riemann tensor (not depending on its derivatives). In general, we want curvature scalars to be scalars that are...

Homework Statement Is there a non-degenerate 2x2 matrix that has only real eigenvalues but is not Hermitian? (Either find such a matrix, or prove that it doesn't exist) Homework EquationsThe Attempt at a Solution Here's my problem. I'm getting Contradicting results. So, I found this 2x2...

Hi, I was wondering if two matrices with the same eigenvalues share the same PDF. Any ideas and/or references would be helpful. Thanks in advance

Show that the eigenvalues of any matrix are unaltered by a similarity transform - the book says this follows from the invariance of the secular equation under a similarity transform - which is news to me. The secular eqtn is found by $$Det(A-\lambda I)=0$$ and is a poly in $$\lambda $$, so I...

I'm almost there in terms of understanding it, but I need to go beyond the text. Here is the example problem: imgur link: http://i.imgur.com/UMj55tF.jpg I can see that where we have 1 = \vec{x}^T A \vec{x} = \lambda \vec{x}^T \vec{x} that 1=\lambda \vec{x}^T \vec{x} = \lambda ||\vec{x}||^2...

Homework Statement Find the eigenvalues of the matrix ## \left( \begin{array}{cc} 3 & -1.5\\ -1.5 & -1\\ \end{array} \right) ## It's probably a really stupid mistake, but the answer I get doesn't match the answer from wolfram alpha's eigenvalue calculator... always a bad sign. Homework...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] Let A be a square matrix of order n such that A^2 = I a) Prove that if -1 is the only eigenvalue of A, then A= -I b) Prove that if 1 is the only eigenvalue of A, then A= I c) Prove that A is...

So, in a section on applying Eigenvectors to Differential Equations (what a jump in the learning curve), I've encountered e^{At} \vec{u}(0) = \vec{u}(t) as a solution to certain differential equations, if we are considering the trial substitution y = e^{\lambda t} and solving for constant...

MIT OCW 18.06 Intro to Linear Algebra 4th edt Gilbert Strang Ch6.2 - the textbook emphasized that "matrices that have repeated eigenvalues are not diagonalizable". imgur: http://i.imgur.com/Q4pbi33.jpg and imgur: http://i.imgur.com/RSOmS2o.jpg Upon rereading...I do see the possibility...

Hi can someone direct me to a free software to calculate eigenvalues and normalized eigenfunctions of a linear integral operator. I am trying to solve a fredholm integral equation with degenerate kernel using it instead of linear equations thanks sarrah

Homework Statement Consider the space ##P_n = \text{Span}\{ e^{ik\theta};k=0,\pm 1, \dots , \pm n\}##, with the hermitian ##L^2##-inner product ##\langle f,g\rangle = \int_{-\pi}^\pi f(\theta) \overline{g(\theta)}d\theta##. Define operators ##A,B,C,D## as ##A = \frac{d}{d\theta}, \; \; B=...

Homework Statement find eigenvalues and eigenvectors for the following matrix |a 1 0| |1 a 1| |0 1 a| Homework EquationsThe Attempt at a Solution I'm trying to find eigenvalues, in doing so I've come to a dead end at 1 + (a^3 - lambda a^2 -2a^2 lambda + 2a lambda^2 + lambda^2 a - lambda^3 - a...

Hello everyone! I'm trying to follow a solution to a problem from the book "Problems and Solutions on Quantum Mechanics", it's problem 1017. There's a step where they go on too fast, and I can't follow. I've posted the solution and where my problem is down below. Homework Statement The dynamics...

Suppose we pick a matrix M\in M_n(ℝ) s.t. all its eigenvalues are strictly bigger than 1. In the question here the user said it induces some norm (|||⋅|||) which "expands" vector in sense that exists constant c∈ℝ s.t. ∀x∈ℝ^n |||Ax||| ≥ |||x||| . I still cannot understand why it's correct. How...

What does it mean when it says eigenvalues of Matrix (3x3) A are the square roots of the eigenvalues of Matrix (3x3) B and the eigenvectors are the same for A and B?

Hi there. How would I show that the eigenvalues of a matrix are an invariant, that is, that they depend only on the linear function the matrix represents and not on the choice of basis vectors. Show also that the eigenvectors of a matrix are not an invariant. Explain why the dependence of the...

http://im54.gulfup.com/ZtJZd5.png http://im54.gulfup.com/SJgJXh.png Till now compared with other subjects that I studied by my self, linear algebra is really the toughest one :bow: Anyway, here I found a plane using characteristic eq. which really surprised me since det(M)=1, M is the matrix...

So, I have the matrix: A = -1 -3 3 9 Eigenvalues i calculated to be λ = 8 and 0 Now when i calculate the Eigenvector for λ = 8, i get the answer -1 3 Then when solve for...

Hi, I am trying to solve the problem of finding eigenvalus for a general square symmetric matrix with the QR algorithm. I have understood that this task is much easier if the matrix is in an Hessemberg form, so I have implemented a function that does that with the Housholder method, but I can't...

I want to know what exactly Eigen value imply. What is its Physical significance ? Physical significance of eigen vector? Does eigen value concept apply in signal processing or evalvating frequency response off a system?

Hey guys, I really need your help. I have an exam tomorrow and no idea how to solve this task. Sorry for my bad english (did not use it for a long time). I hope that I translated the task correctly so that you might be able to help me. So We have two particles with spin=1 which means they have...

Homework Statement Find a 2X2 matrix that has all non-zero entries where 3 is an eigenvalue Homework EquationsThe Attempt at a Solution well since the 2x2 matrix cannot be triangular, it makes things harder for me. I have no idea where to start. I am not given any eigenvectors either. It seems...

Hello, I'm having problem understanding this particular part, don't know it seems too dry and behind my capabilities of imagining the problems!, in the same time I feel like there is too many gaps in the way that the book explain the subject. I'm using "Mathematical methods in the physical...

Given the following matrix: 2 3 0 3 2 4 0 4 2 I'm having a difficult time working out the characteristic polynomial. I used the shortcut that I saw on YT, where it is (I am using x instead of lambda) X^3 - (trace) X^2 + (A11+A22+A33) X - DET(A) I got the following: trace is just 2+2+2 = 6...

Homework Statement Look at the matrix: A = sin t sin p s_x + sin t sin p s_y +cos t s_z where s_i are the pauli matrices a) Find the eigenvalues and normalized eigenvectors (are they orthogonal)? b) Write the eigenvector of s_x with positive eigenvalue as a linear combination of the...

Mod note: I revised the code below slightly, changing the loop control variable i to either j or k. The reason for this is that the browser mistakes the letter i in brackets for the BBCode italics tag, which causes some array expressions to partially disappear. Hello, I am trying for the first...

Quantum Eigenvalues have more information contents than non-quantum eigenvalues. What are the different algorithm to extract information from them? For example. If memory chips were made of quantum eigenvalues. How do you read and store information into them?

Homework Statement I have ##A=TST(-1,2-1),## and I need to show that an eigenvector of A is,##Y_{j}=sin(kj \pi / J).## and then find the full set of eigenvalues of A. The matrix A comes from writing ##-U_{j-1}+2U-U_{j+1}=h^{2}f(x_{j}), 1\le j \le J-1##, in the form ##AU=b## Homework...

Homework Statement I have 4 equations. 3x+6y-5z-t=-8 6x-2y+3z+2t=13 4x-3y-z-3t=-1 5x+6y-3z+4t=-6 I have already solved this matrix using gauss elimination and found that x=1, y=2, z=5, t=-2 Now the next part of the question asks to solve the matrix using eigenvalues and eigenvectors...

Consider the system: $x' = x + y + z$ $y' = 0x + 2y + 3z$ $z' = 0x + 0y + 3z$ a)Find the eigenvalues for the systemSo after doing my $3 \times 3$ matrix I got: $\lambda_1 = -3$, $\lambda_2 = 1$, and $\lambda_3 = 2$ , is this correct? b)Find an eigenvector for the smallest eigenvalue So I am...

Consider the system $x'_1 = x_1 + 2x_2$ and $x'_2 = 3x_1 + 2x_2$ If we write in matrix from as $X' = AX$, then a) $X =$ b) $X' =$ c) $A =$ d) Find the eigenvalues of **A**. e) Find eigenvectors associated with each eigenvalue. Indicate which eigenvector goes with which eigenvalue. f)...

Hi, I'k looking at some MATLAB code specifically eig2image.m at: http://www.mathworks.com/matlabcentral/fileexchange/24409-hessian-based-frangi-vesselness-filter/content/FrangiFilter2D So, I understand how the computations are done with respect to the eigenvector / eigenvalues and using...

i suppose matrices of the form $$A_i=\left(\begin{array}[cc] ccos(x_i)&sin(x_i)\\sin(x_i)&-cos(x_i)\end{array}\right)$$ And i consider the matrix $$C=A1\otimes A2\otimes 1_4-A1\otimes 1_4\otimes A2$$ I would like to show that the eigenvalues of C are independent of the x i tried with...

Consider the system $x'_1 = -5x_1 + 1x_2$ $x'_2 = 4x_1 - 2x_2$ If we write in matrix form as $X' = AX$ then a) X = b) X' = c) A = d) Find the eigenvalues of A. e) Find eigenvectors associated with each eigenvalue. Indicate which eigenvector goes with which eigenvalue. f) Write the...