Questions tagged [eigenvalues]

Questions on symbolically or numerically determining the eigenvalues of matrices (Eigenvalues, Eigensystem) or differential equations (DEigenvalues, DEigensystem, NDEigenvalues, NDEigensystem) in Mathematica. Also includes determining the eigenvalues of differential equations with DSolve or NDSolve.

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4
votes
1answer
90 views

Eigenvalue of Hofstadter spectra

This the code of Hofstadter spectrum for square lattice using Mathematica ...
-1
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0answers
47 views

Problem with KarhunenLoeveExpansion's output

I have a matrix called realizationMat, it contains 101 measurements of 90 realizations of a stochastic process. I will post instead an abridged 11*5 smaller example ...
2
votes
2answers
56 views

How can I store vectors in a matrix

I am triying to generate realizations of a Gaussian random process using the KL expansion. For that, I need to multiply an eigenvector for an eigenvalue and a random variable. I have tried ...
2
votes
1answer
105 views

Solving simultaneous differential equations using eigen value method

I wish to solve the following set of ODE. $$i\frac{d}{dt}B_{n}\left(t\right) =f\sqrt{\left(P-n\right)\left(n+1\right)}B_{n+1}\left(t\right)+f\sqrt{n\left(P-n+1\right)}B_{n-1}\left(t\right) + Y\left[...
1
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0answers
33 views

NDEigensystem solutions depend on how many solutions I ask for?

Background I am using NDEigensystem to solve the following eigenvalue problem: $$ \left( \begin{matrix} m&-i\partial_x \\ -i\partial_x & -m\end{matrix}\right) \left( \begin{matrix} u_u(x) \\ ...
3
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0answers
172 views

Chladni experiment verification

I refurbished my post in order to be more understandable. After computing simulations of Chladni patterns with Mathematica (see my previous topics), I finally went to practice. I realized my own ...
0
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0answers
46 views

How to find eigenvalues of 8x8 matrix?

I am new to Mathematica, and was trying to find the eigenvalues of an 8x8 matrix using Mathematica. I have fairly simplifies the matrix A into a mathematical expression and I know the final ...
0
votes
1answer
37 views

Mathematica returns an empty plot for the real part of the eigenvalues [closed]

I have a 3*3 matrix. Using Mathematica I have found the eigenvalues in terms of "K". The problem arises when I'm plotting the real part of eigenvalues against "k" (k is a positive ...
4
votes
2answers
117 views

How to generate the 8^th order symmetric binary matrices whose sum of absolute eigenvalues is 8?

It is needed to generate all 8th order(8 by 8) symmetric binary matrices(of 0's and 1's) such that the sum of the absolute eigenvalues is 8. Listing all the 8th order symmetric binary matrices and ...
6
votes
2answers
167 views

2D Chladni patterns realistic animation

My wish is to create a (realistic) animation of the patterns appearing during the Chladni experiment. I tried something, but it is not continuous because it is based on the eigenmodes, so the ...
1
vote
0answers
42 views

Eigenvalues of a 6x6 matrix [duplicate]

Eigenvalues[{{0, A, 0, B, 0, D}, {-A, 0, -C, 0, -EE, 0}, {0, C, 0, A, 0, B}, {-B, 0, -A, 0, -C, 0}, {0, EE, 0, C, 0, A}, {-D, 0, -B, 0, -A, 0}}] I am ...
0
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1answer
59 views

NDEigensystem does not evaluate

I am trying to obtain the eigenvalue of a certain $4\times 4$ matrix differential operator. The region I consider is a rectangle of size $5\times 200$. At left and right side, I applied the periodic ...
0
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1answer
59 views

Number of elements in a list [closed]

I have written the following program in mathematica. ...
3
votes
1answer
243 views

Laplace's problem in Mathematica

I am computing the Laplace's eigenvalue problem on the region $\Omega$ formed by the four vertices $(1,1),(1,2),(−1,2),(−1,1)$. Consider the Laplace problem, $$-L u = \lambda u$$ where $$L = y^2 \Big( ...
0
votes
0answers
43 views

Find the eigenvalues for 3 equations after variable separation

I have to find the eigenvalues for three functions obtained with variable separation method. The functions result from the following expression: I tried with the following code: ...
1
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0answers
39 views

Find eigenvalues for a basic equation [closed]

I have to check if I can get the eigenvalues for a specific equation. Actually I just want the first 2 beta: eqy = Y''[y] + \[Beta]^2*Y[y] == 0; So I've tried to ...
1
vote
1answer
62 views

Solving an eigenvalue problem

I am computing the eigenvalues of Laplacian-type operator on the unit square $\Omega = [0, 1]^2$ Consider the eigenvalue problem on the unit square $\Omega$, $$-L u = \lambda u$$ where $$L = e^{2y} \...
0
votes
0answers
33 views

List of eigenvalues not exceeding a given number

I am interested in computing the eigenvalues of Laplacian numerically. Consider the $\textbf{LAPLACE'S BOUNDARY VALUE PROBLEM ON A UNIT SQUARE:}$ Let $\Omega = [0 , 1]^2$. Now the eigenvalue problem ...
4
votes
2answers
150 views

Asymptotic law in Laplace's problem

$\textbf{Eigenvalue problem on a unit square $\Omega = [0,1]^2$ :}$ Consider the eigenvalue problem with the Dirichlet boundary condition that is, $$-Lu = \lambda u$$ where $$L = \frac{\partial^2}{\...
1
vote
0answers
68 views

Multiplicity in Laplace's Eigenvalue Problem

I am computing Laplacian on a unit square $\textbf{numerically}$. Consider the eigenvalue problem on $\Omega = [0 , 1]^2$ $$-Lu = \lambda u$$ where $$L = \frac{\partial^2}{\partial x^2} + \frac{\...
3
votes
1answer
185 views

Solving a Eigenvalue Problem

$\textbf{Eigenvalue problem on a unit square $\Omega = [0,1]^2$ :}$ Consider the eigenvalue problem with the Dirichlet boundary condition that is, $$-Lu = \lambda u$$ where $$L = \frac{\partial^2}{\...
3
votes
1answer
164 views

How can I use Tally in my code?

I a computing the eigenvalues and eigenfunctions of a Laplacian on a unit square. I have written it as follows: ...
0
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1answer
82 views

How to write matrix elements in Mathematica? [closed]

For a matrix $A$, one computes the $ij$-$th$ matrix elements in a basis $\{|e_i\rangle\}$ as $$A_{ij} = \langle e_i|A|e_j\rangle$$ How can one implement this in Mathematica? As an example, consider a ...
0
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0answers
15 views

QR algorithm implementation for eigensystem - where is error [duplicate]

I implemented the simplest possible program of QR algorithm, but the program gives wrong solutions, i.e. eigenvalues (diagonal elements of converged matrix x) and ...
1
vote
1answer
172 views

Program for computing Weyl's law

I have calculated the solution to the Laplacian eigenvalue problem on the unit square $\qquad - \Delta u(x,y) = \lambda u(x,y) \text{ on } {[0,1]}^2$ with the Dirichlet's boundary condition ($u = 0$). ...
4
votes
1answer
48 views

Removing Sharp Peaks from NDEigensystem Results

I have an eigensystem I am trying to solve using NDEigensystem, so as a test I am using a different operator which is known to admit to analytical solutions which are smooth(i.e., no discontinuities ...
0
votes
1answer
50 views

How I can find the eigenvalues and eigenvectors of 500 matrices with 3x3 dimensions? [closed]

I can apply the Eigensystem command to a single matrix and it worked fine. But it takes me too much time. I want to get the eigenvalues and eigenvectors of multiple 3x3 matrices at the same time. ...
2
votes
3answers
37 views

Repeated ReplacePart On Each Element of a Square Matrix for Eigenvalue Difference

I have a large $n\times n$ square matrix, whose elements are all either 0 or 1. I want to see by how much the single largest eigenvalue of the matrix (which Mathematica gives as the first element in ...
3
votes
2answers
300 views

Speedup calculation of the largest eigenvalue and eigenvector of a 400×400 matrix? [duplicate]

Actually, the matrix is an adjacency matrix of a network. The code is: ...
3
votes
1answer
67 views

Getting different eigenvectors for same matrix? [closed]

I have the same two matrices, one has the input values as integer and the other as real numbers. Mathematica shows the eigenvectors are completely different for the two same matrices and wondering ...
6
votes
4answers
271 views

FindInstance won't compute this simple expression

I want to find instances where this standard 3x3 symmetric matrix has only positive eigenvalues. So I run ...
5
votes
1answer
151 views

How to compute the trace distance of a density matrix

I am trying to compute the trace distance of two general $4 \times 4$ density matrices as such: $D=\frac{1}{2} \, \mathrm{tr} \, |\Delta\rho|_1$ where $\Delta\rho$ is the difference between two ...
1
vote
1answer
47 views

Ordering eigenvectors for basis transformation

Let's say I have a matrix $H$ represented in some basis, $a$, and I'd like to transform this to be represented in a different basis, $b$. The only difference between the bases is that $b$ is a basis ...
2
votes
1answer
177 views

Numerical solution of Eigenvalue equation

I am interested in finding eigenvalues of Schrödinger-type equations, a prototype example being $$- w^{\prime \prime } (y) - 6 \operatorname{sech}^2 (y) w(y) + w(y) = \lambda w(y)$$ I posted a ...
7
votes
0answers
220 views

Numeric Solution Hydrogen Atom

I'm trying to solve the Schrödinger equation for the hydrogen atom without made the variable separation of the polar and radial coordinate. It is my test code to extrapolate to another system with its ...
3
votes
3answers
347 views

Solving a Sturm-Liouville problem

Ello, I would like to reproduce the analytical solution of the following eigenvalue problem, or at the least confirm them numerically (especially the eigenvalues): $$ - \frac{1}{2} y^{\prime \prime} ...
0
votes
1answer
50 views

Plot Eigenvalues with respect to a parameter

I have a parametrical matrix (18x18) which I want to plot its eigenvalues with respect to a parameter. For simplicity, lets assume that it is instead a 3x3 matrix which is not fully numerical but ...
1
vote
1answer
74 views

Lowest Eigenvalue of a large sparse matrix without choking up the RAM (Corrected) [closed]

I am trying to find the lowest eigenvalue of a large sparse matrix of dimension N (=$3^n$, where n is number of particles in system ) using ...
4
votes
1answer
92 views

Sort eigenvectors by eigenvalue and assign to variables

I have the following question: Let T = {{0, 0, 2}, {0, 0, 0}, {2, 0, 3}}, I know that its eigenvalues, in a decreasing order, are 4, 0 and -1. Mathematica displays ...
1
vote
0answers
32 views

How to speed up this code (finding eigenvector with smallest eigenvalue)? [closed]

I have following code. The function TraceSystem is to take partial trace of matrix and I think this part is fine. The main code is below in dd and I think the main problem is in here for Eigenvector. ...
0
votes
0answers
25 views

Solving quadratic eigenvalue problem [duplicate]

I am trying to solve a quadratic eigenvalue problem using Mathematica similar to Matlab command "polyeig" https://www.mathworks.com/help/matlab/ref/polyeig.html How to do it using ...
2
votes
0answers
70 views

What is the fastest way to get the lowest eigenvalue and corresponding eigenstate in Mathematica?

I tried to use the Arnoldi method to get the smallest eigenvalue and corresponding eigenstate for large matrix. However, Arnoldi did not give me the desired result: ...
4
votes
2answers
229 views

NDEigensystem and radial function equation for Hydrogen atom

I'm trying to numerically solve the radial equation for the 3D hydrogen atom problem, i.e., to find $R(r)$ which satisfies: $$ -\frac{\hbar^2}{2m}\left[\frac{1}{r}\frac{d}{dr}\left(r^2\frac{dR(r)}{dr}\...
-2
votes
1answer
51 views

Sorting of eigensystem accroding to specific eigenvector

I have a matrix, I want to sort it with respect to specific eigenvectors. Here, I provided an example of a matrix HT: ...
0
votes
1answer
89 views

Having problem in evaluating the eigenvalues of an $11\times11$ symmetric matrix in Mathematica [closed]

I am solving an $11\times11$ matrix in Mathematica. I am facing problem when I try to find the determinant or eigenvalues of this matrix. The error (Det::matsq/<...
8
votes
2answers
206 views

Why Mathematica gives wrong eigenvalues for this equation?

Here is an eigenvalue problem in cylindrical coordinate: $$\mu(r)\frac{\partial}{\partial r} \left( \frac{1}{\mu(r)}\frac{1}{r}\frac{\partial (ru)}{\partial r} \right)=-p^2u$$ where p is the required ...
2
votes
1answer
100 views

Sorting Eigensystem According to Complicated Rule

I have looked for an answer to this but the near duplicates I could find seemed slightly distinct. I have a matrix $A$ which has eigenvalues in pairs $\lambda_1,-\lambda_1,\lambda_2,-\lambda_2,\dots$. ...
0
votes
1answer
46 views

Why is Mathematica not simplifying further even after providing assumptions?

m = {{0, 0, 1, 0}, {0, 0, 0, 1}, {-5 X^2, X^2, 0, 0}, {X^2, -X^2, 0, 0}}; Simplify[Eigenvalues[m], Assumptions -> X>0] The output I get is this below. The ...
0
votes
1answer
105 views

Transforming a full $4\times4$ symbolic matrix into a full $3\times3$ matrix and an eigenvalue

I have a $4\times4$ matrix A=\begin{pmatrix} 0.16 (\cos (\text{kx})+2) & 0.55 \cos \left(\frac{\text{kx}}{2}\right)+(0.\, +0.76 i) \sin \left(\frac{\text{kx}}{2}\right) & 0.55 \cos \left(\...
2
votes
1answer
122 views

NDEigensystem to solve differential equation

When trying to solve the differential equation radialEqdouble[k_] = f''[u] + k*u^2*f[u] - u^4*f[u] where k is a constant, I am able to produce a plot consistent ...

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