# 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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1answer
90 views

### Eigenvalue of Hofstadter spectra

This the code of Hofstadter spectrum for square lattice using Mathematica ...
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 ...
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 ...
1answer
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0answers
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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
1answer
59 views

### Number of elements in a list [closed]

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

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 ...
2answers
150 views

1answer
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1answer
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### 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 ...
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 ...
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 ...
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. ...
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 ...
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: ...
2answers
229 views

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 $\lambda_1,-\lambda_1,\lambda_2,-\lambda_2,\dots$. ...
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 ...
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(\...
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 ...