Questions tagged [eigenvalues]

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35 views

Finding the Eigenvalues for big matrices

To start I have the following matrix (not so big) I want to find the Eigenvalues in terms of kx and ky. I tried to use the classical ...
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1answer
106 views

Plotting eigenvalues

I am trying to reproduce figure 10 in the linked paper. The authors have used Matlab bvp4c function to find multiple solutions for the system of ODE and then carried out the stability. Here is my ...
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2answers
61 views

Problems with spectral decompositon of a $4 \times 4$ matrix [duplicate]

Given a matrix $M$ with eigenvalues $\lambda_1, \lambda_2, \lambda_3,\lambda_4$ and the corresponding eigenvectors $|v1\rangle,|v2\rangle,|v3\rangle,|v4\rangle$. One can write $ M = \lambda_1 |v1\...
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102 views

Eigenvalues of a fourth-order ODE

Consider the following ODE for $y(x)$ over $x\in\left[0,\frac{1}{2}\right]$ with an eigenvalue $\lambda$ $\qquad 2x\,y''''+ 4y'''=\lambda\, y''$ The boundary conditions at $x=\frac{1}{2}$ are $y'\...
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1answer
72 views

Proving the positive semidefiniteness of a 6X6 symbolic matrix

Specifically, I want to check the positive semidefiniteness of the following 6X6 symbolic matrix ...
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1answer
66 views

Problem with QRDecomposition [closed]

I was using Mathematica for the QR decomposition method. But I got strange results. I wanted to find eigenvalues of a matrix, say ...
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2answers
95 views

Different result from utilizing of eigenvalues and eigenvectors commands

I have a matrix as a function of a parameter like ...
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20 views

Using Eigensystem to solve eigenvalue problem [duplicate]

I'm trying to solve an eigenvalue problem of the form: $\textbf{A}\vec{x}=\lambda \textbf{B}\vec{x}$, where A and B are square matrices, $\lambda$ are the eigenvalues and $\vec{x}$ the eigenfunctions. ...
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1answer
84 views

Eigenvalues and numerical eigenfunctions for similar differential operators

I am looking to numerically approximate the eigenvalues and eigenfunctions for a differential operator I am working with, assuming $\pi$ periodic boundary conditions. Namely, I define the function $...
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27 views

What kind of performance should I expect out of Eigensystem using FEAST?

I'm numerically solving a time-independent Schrödinger equation using Eigensystem's FEAST method. It takes a lot longer than I ...
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2answers
146 views

Finding specific eigenvalues

Given an $n\times n$ matrix $Q$ (with e.g. $n\approx10^4$) I am only interested in the 3rd smallest eigenvalue of $Q,$ and not the entire spectrum (assume all eigenvalues are real, e.g. a Hermitian ...
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0answers
111 views

Somewhat Singular Sturm-Liouville Equation (With Edition)

I am trying to solve the following Sturm-Liouville equation (i.e., plot the eigenfunctions and calculate the eigenvalues): $$\frac{d}{dx}\left(x²\frac{d}{dx}\right)f(x) + 2f(x) = -\lambda x²f(x)\,,$$ ...
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1answer
71 views

“Arnoldi” method for Eigenvalues inside FindRoot

I'm trying to implement a function which, given a matrix with one free parameter, would return the value of the parameter at which the lowest eigenvalue of the matrix is equal to a certain number. ...
3
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1answer
79 views

Finding eigenvalues of the Laplacian on solenoidal (divergence-free) vector fields

In Mathematica it is easy to find eigenvalues of the Laplacian in simple cases. For example, on $\Omega\in \mathbb{R}^2$: ...
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34 views

Trying to extract the Eigen values and Eigen vector of a matrix

I have a Matrix A, which is a function of ω. I wanted to find the eigenvalues and eigenvectors of this matrix, how to do it. I have used the EigenSystem function ...
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2answers
122 views

Finding eigenvectors of a differential operator

How can I find the eigenvalues and eigenvectors(numerically) of the below matrix equation: $ \qquad \hat{A}\left({\begin{array}{c} y_1(x,\theta)\\ y_2(x,\theta) \\ \end{array} } \right)= ...
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2answers
69 views

Checking NDEigensystem Results

I'm looking to verify the output of a call to NDEigensystem. I'm doing this by plotting the operator acting on the Interpolating Function outputs versus the ...
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0answers
53 views

Block diagonalizing a complex anti-symmetric matrix

I am going to evaluate the block diagonal form of few skew-matrices. When matrix elements are real I can simply follow the approach suggested in this thread which I have implemented that as ...
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2answers
54 views

Trying to to replace Root expressions from the output of Eigenvalues by the explicit forms

When I calculate the eigenvalues of the following matrix (H) by using Eigenvalues, I get complex expressions with ...
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0answers
104 views

Why doesn't NDEigenSystem give smooth eigenfunctions? [closed]

I'm looking for smooth solutions of the 1D Helmholtz equation $\left[\frac{d^{2}}{dx^{2}}+k_{0}^{2}\epsilon(x)\right]\phi=0$ with homogeneous Dirichlet boundary conditions, where the permittivity $\...
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3answers
196 views

Eigenvectors in the limit $ \mu\rightarrow 0 $ are not the same as eigenvectors when setting $ \mu=0 $ from the beginning

I would like to find the eigenvectors of a matrix and see what the eigenvectors look like in the limit of $ \mu\rightarrow 0 $: ...
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1answer
54 views

Remove +0Is from Root function

I'm trying to find the zeros of the eigenvalues (functions of $k_x$) of a self-adjoint $4\times4$ matrix H: ...
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1answer
47 views

Trace change of one single value in a list

I have a list of eigenvalues, say: list1 = {10., 9., 9., 8.5, 7.5, 6.5, 6.1, 5.6, 4.5, 4., 4., 3.8, 3., 3., 1., 1., 1., 0.8, 0.5, 0.5} After slightly modifying ...
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1answer
101 views

Problem with complex eigenvalues in periodic Sturm-Liouville problem

I'm having trouble using NDEigenvalues to obtain the first few eigenvalues for a differential operator on the circle of radius one-half. $\qquad Lf(x) = f''(x)+ (-...
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0answers
34 views

Getting a non zero determinant of matrix R, when the Rank of R is not equal to Dimension of R

I have a square matrix whose dimensions is 9 cross 9, when I extract the rank of the matrix R, I am getting rank as 6. I have constructed R matrix by minimizing the Lagrangian Lg with respect to a[1].....
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27 views

Sequential production of Eigenvectors?

I have to deal with very large matrices in Mathematica (dimensions $10^4\times10^4$ at least). Obtaining the eigenvalues of these matrices is not so difficult since, it is not memory intensive or ...
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1answer
71 views

find a maximum parameter for a range of target eigenvalues as a function of matrix dimension

I have a symbolic tridiagonal matrix of this form ...
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2answers
940 views

Two matrices that are not similar have (almost) same eigenvalues [closed]

I have two matrices $$ A=\begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix} \quad \text{ and } \quad B=\begin{pmatrix} d & e & f \\ d & e &...
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1answer
90 views

How can I get the Eigen system of a certain matrix? [closed]

How can I get Eigen system of c, where c = a - iota * b? Please help me to find the Eigen system in a nice form. ...
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0answers
65 views

Derivative of eigenvalues

I work with 4x4 Hermitian matrices (r). I want to calculate a derivative of a function f[t,r] (ff[t_,r_]=1/2*D[f[t,r],t]), where the function f depends on the absolute value of the eigenvalues of r. ...
3
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2answers
766 views

Problem with Eigenvectors

When I want to calculate eigenvectors of the following matrix in Mathematica the only answer it gives me is zero vector, anybody knows how to fix this? here's my matrix : \begin{equation} X=\left(\...
5
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2answers
117 views

How to show just one function from a stored plot?

Q: Is there a general way to remove particular functions from a previously stored call to a plot function? Here is a specific example: ...
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0answers
275 views

DEigenvalues and NDEigenvalues return different values

In the following example, DEigenvalues and NDEigenvalues return different results despite having identical arguments. Does anyone know why? (I use Mathematica 11.3) ...
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1answer
132 views

How to solve this 1st-order linear ODE system with a few discrete eigenvalues?

I am trying to solve the eigensystem of a 1st-order linear ODE system in the region $(-\infty,\infty)$ and with Dirichlet boundary condition at the infinities $$ -i\partial_xu(x)+f^*(x)v(x)=\lambda u(...
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68 views

How to draw mode vectors of two degrees of freedom

Here is two degrees of freedom system. *And the mode vectors of this system is ({{1, 1},{1, -1}}) *And the mode shape will be expressed like this... And the ...
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129 views

Finding eigenvalues of a differential operator

I am trying to get the eigenvalues of the following differential operator $$L\psi(r) = -f \partial_r (f \partial_r \psi(r)) + V \psi(r)$$ which must satisfy (obviously) $$L \psi(r) = \omega^2 \psi(...
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40 views

Some issues with DEingesystem

I would like to solve (get its eigenvalues/vectors) the Sturm-Liouville problem, for the following differential operator: $L =\partial_{r} \partial_{r} \psi(r)$. Also, I would like to impose the ...
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52 views

Eigenvectors of Hermitian matrices [duplicate]

I asked a similar question in the physics stack exchange, but realized my question is probably more suited here. For any Hermitian matrix $H = H^{\dagger}$ we can write $H = P DP^{\dagger}$ where $P$ ...
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0answers
33 views

Ordering of Eigenvectors [duplicate]

I am interested in computing the derivatives of the eigenvalues of a certain $n\times n$ Hermitian matrix $M(t)$. I know I can do this easily since I know the exact expression for $\dot{M}$, and the ...
4
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2answers
224 views

Help with coding a matrix

I have a $n \times n$ matrix $A$ with a full set of eigenvalues $\lambda$ including repetitions. I want to create the following $i \times i$ matrix: $$\left(\sum_{a=2}^i (a-1) |a-1⟩⟨a| \right) + \...
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1answer
148 views

Eigenvalue problem

my question is about solving an eigenvalue problem of the Helmholtz equation using sinc approximation $\nabla^2E + V (x) = \lambda E$ and $V(x)= X^2 / 2$ I have a problem in calculating the ...
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2answers
89 views

How to get eigenvectors of a 4x4 matrix? [closed]

MatrixForm[m = {{2, 9, 0}, {3, 8, 9}, {3, 9, 1}}] Eigensystem[m] I am facing problem in finding eigenvectors using ...
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0answers
18 views

Solve, store, and access eigenvalues and eigenstates of M[x,y], for various points {x,y}

I'm interested in solving a position dependent eigenvalue problem for matrix M[x,y], where {x,y} is some discretized set of points. I may need to access the eigenstates and eigenvalues multiple times ...
5
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2answers
207 views

Lowest Magnitude Eigenvalues of Large Sparse Matrices

I am trying to find the first three lowest eigenvalues of large sparse matrices of size range $10^3 - 10^5$. The matrices depend on some parameter $x$, so I first construct the matrices and then use ...
8
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3answers
607 views

How to set interface conditions for optical waveguide in NDEigensystem?

I have been working on waveguide mode analysis using FEM in Mathematica for a week, but I haven't succeeded until now. The optical fiber-like waveguide is featured with different refractive index in ...
0
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1answer
59 views

Time used by Mathematica to calculate tridiagonal matrix

I have a question. I need to find the eigenvalues and eigenvectors of a tridiagonal matrix of size NxN. Can you tell me how much time does Mathematica need to do that in minutes? for Size N ...
5
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1answer
83 views

How to change the default normalization for NDEigensystem?

I'm currently using NDEigensystem to solve a PDE that describes a particle travelling on a hyperbolic (negatively curved) surface. However, the eigenfunctions that are returned by NDEigensystem are ...
5
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1answer
582 views

How to plot the eigenvalues of a parametric matrix efficiently?

I was wondering how can I set the variable type of matrix elements to be real. The problem is, I creat a variable-dependent matrix as follows and I get the eigenvalues now I want to plot the ...
3
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1answer
74 views

How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?

Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows. ...
38
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2answers
1k views

Eigenvalues broken in Version 12.0

Bug introduced in 12.0. The following code calculates the eigenvalues of a certain complex matrix, which come in pairs of opposite complex numbers. Therefore one can check whether the sum of all ...