# 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.

395 questions
Filter by
Sorted by
Tagged with
67 views

### NDEigensystem: 1D problem with discontinuous coefficients

I am trying to use NDEigensystem to solve the 1D problem -cs[x]^2 vx''[x] = w^2 vx[x] with vx[x] and w the eigenfunction and eigenvalue. The coefficient cs[x] is discontinuous at x = -xp, +xp and vx[x]...
291 views

### Linear ODEs with NDSolve

I am trying to solve some first order linear odes. My code is below: ...
31 views

### Graphing multiple functions on the same graph using AbsArgPlot, but the colour of the graphs keep coming up grey

I am trying to create a plot of the modulus of the eigenvalues of an associated matrix that is parameterised by sigma. When plotting a single eigenvalue using AbsArgPlot, the graph is coloured nicely ...
32 views

### Generate a random matrix with a condition on its eigenvalues

I can generate Radom matrices using mat = RandomReal[{-1, 1}, {2, 2}]; But how can I generate the mat matrix so that the ...
59 views

### Eigenvalues aren't given to be imaginary

So I have this matrix I am working with that looks like $$S=\begin{pmatrix}0 & -a & b\\ a & 0 & -c\\ -b & c& 0 \end{pmatrix}$$ and upon asking mathematica for the eigenvalues ...
75 views

### Check Eigenvalues and Eigenvectors are correct [closed]

I have a matrix: J = {{0, -λ (1 + φ)/τ}, {-(1 + φ)/τ, δ}}; And I compute the Eigenvalues and Eigenvectors as follows: ...
102 views

### NDEigensystem returns reversed list of eigenfuctions

I'm considering the two coupled linear differential operators ...
45 views

### How to use DEigensystem with Dirichlet Condition an NeumannValue

How can I use DEigensystem to obtain eigenvalues and eigenfunctions for differential operators in two dimensions for the follwing problem Examples in Wolfram documentation only consider Dirichlet <...
107 views

### How to solve 2D eigenvalue problem with robin boundary conditions

I need to solve an eigenvalue problem in 2D as seen in the picture. I've tried the function NDEigensystem but reading its documentation it seems it has issues with ...
1 vote
90 views

### Discrepancy in eigenvalues [closed]

I need to calculate the eigenvalues of a matrix and the parameters are such that there is a large difference (several orders of magnitude) between the entries. Theoretically, the matrix has only one ...
143 views

### NDEigensystem with FEM: parasitic solutions

I am trying to find the eigensystem of a system of 3 coupled ODEs. Analytically, the system spectrum should have a gap at [-2M,2M] (except for the degenerate state with E=0, strictly at the middle of ...
1 vote
20 views

### Why does Sparsearray diagonalization by Krylov technique become slower for very large sizes?

Here is an example sparse matrix, taken from example Hamiltonian, which was a question I asked before in this forum. ...
427 views

### Mathematica produces seemingly wrong eigenvalues and eigenvectors

I have a Fredholm kernel defined on [-1, 1], which is symmetric under transformation (x, y) -> (-x, -y): k[x, y] == k[-x, -y] ...
79 views

### Optimising eigenvalue matrix calculation

I'm quite new to mathematica and am trying to figure out how to optimise my code as currently it takes a very long time to compile and makes it hard to bug test. The first part that creates the graph ...
1 vote
57 views

### Intel MKL ERROR: Parameter 2 was incorrect on entry to ZGEHD2

I have some code which is diagonalising very large random matrices, and storing certain statistical properties of their eigenvalues and eigenvectors. The code runs fine on my computer. When running it ...
65 views

### Efficiently calculating half of the eigenvectors of a sparse array

Eigenvectors of a sparse array $\quad$ Problem statement I want to calculate the eigenvectors corresponding to the negative eigenvalues of an $8L^2 \times 8 L^2$ matrix ($L \sim 30 )$. Most of the ...
89 views

### Why does adding a decimal point change the eigenvector? [closed]

I am computing the spectrum of a matrix: When I add a decimal point to the argument, then one of the eigenvectors corresponding to the eigenvalue 2 turns out to be different in the two cases. What is ...
1 vote
39 views

### Eigenvalues broken for nonsymmetric matrices

It looks that eigensystem calculation can easily go broken with real nonsymmetric/general complex matrices. Here are two examples with the possibly complex spectra plotted in the complex plane. I'm ...
182 views

### Unbounded solution at boundaries with few combination of values in this BVP solution

I had asked a question here regarding solution to a BVP problem. bbgodfrey provided an excellent answer using the method of integrated least squares. However, for a few specific set of values of ...
227 views

### Inconsistent behaviour between Active and Inactive forms of PDEs (finite element method)

I have been using the finite element tools in Mathematica version 13.0 to solve eigenvalue problems in physics (Schrödinger equation) using NDEigensystem, but I am having some issues with non-...
1 vote
80 views

### How to give range of values while using NDEigensystem for a 2D Schrödinger equation?

This program runs fine and I am able to get eigenvalues and eigenfunctions, however, I want to give a range of values for x and y. Can you suggest, how to edit my code for that? ...
133 views

### Could all eigenvalues of this matrix be positive?

I have the following list $\beta$ with 5 equations ...
73 views

### How to use NDEigensystem to find eigenfuction and Eigenvalues of 1D Harmonic Oscillator? [closed]

Where am I wrong? Eigenfunctions and Eigenvalues are coming out fine, but while doing the integration, I am facing difficulties. ...
164 views

...
97 views

### Does current Mathematica capability allow solving PDEs (e.g. reaction diffusion equation) over surface of a mesh or surfaces

I came across this nice paper (https://arxiv.org/pdf/1605.01583.pdf) where the authors simulated a reaction diffusion system over the surface of a gecko, primarily to understand how various patterns ...
227 views

### Eigenvalue problem with NDSolve

I am trying to solve the following system of linear ODEs. It is an eigenvalue problem. ...
136 views

...
77 views

...
50 views

### List of eigenvalues of a list of abstract states

Suppose I have the states \Psi, \Phi and \Zeta and I also have the following relations given ...
108 views

### Solving boundary value problem with coupled odes at interface

I am trying to get the eigenvalues of the following differential system ...
73 views

### How to find the characteristic vibration frequencies of a system with any number of masses and springs using eigendecomposition?

I have created a program to solve any system of three springs and two masses using Mathematica's Eigendecomposition functions. My goal is to solve a generalization of the spring system presented in ...
77 views

### Using the result of NIntegrate as a potential in NDEigensysem

I am trying to find the eigenvalues and eigenstates of a Hamiltonian with a potential which cannot be analytically defined. In particular, it is the integral of the product between two functions: <...
1 vote
95 views

### How to improve accuracy of calculating eigenvalues of Non-Hermitian matrix?

I have a non-Hermitian Matrix nonHM whose size is $n \times n$ and is a function of $c1$.the Eigenvalues are symmetric with ...
448 views

### Library for FEAST method is missing

Mathematica (V 12.3.1, Native Mac M1 version) is not letting me use the FEAST method for solving eigenvalue problems. For example, ...
120 views

### Find relationship between parameters to prove conditions of eigenvalues

I have the following 3-by-3 matrix. I need to find condition(s) on the parameters 'a' and 'b' such that this matrix has exactly 1 eigenvalue bigger than 1 in absolute value and other two eigenvalues ...
609 views

### Routh-Hurwitz criterion not giving correct answer when done manually?

Consider the system: \begin{align} \frac{dS}{dt} &= \nu N -\frac{\beta S I}{N} + \xi R - \nu S\\ \frac{dE}{dt} &= \frac{\beta S I}{N}- \sigma E -\nu E \\[2ex] ...
1 vote
24 views

### 'Tag in is protected' error in eigenvaules for large size Hamiltonian [closed]

I am trying to compute the eigenvalues for any size Hamiltonian matrix. To do this, I first manually compute the first few cases for N=2,3. However, when I want to see what happens for N=4, I meet ...
1 vote
68 views

### Obtaining more values from NDEigenvalues

When I run this code ...
69 views

### Construct a matrix from its elements and solve the eigenvalue problem

I want to construct a 10 by 10 matrix whose elements are given by $$H_{nm}=\delta_{nm}\left (n^2+v[b_1-b_0-h(2m,b_0,b_1)]\right) \\ +v(1-\delta_{nm})\left (h(n-m,b_0,b_1)-h(n+m,b_0,b_1)\right)$$ ...
80 views

### Problem with the plots of eigenvalues of the Matrix

I am trying to plot the eigenvalues of the following matrix ...
34 views

### Using Maximize function with UnitaryMatrixQ constraint

Define a function ...
Consider the following eigenvalue equation $$-\frac{d^2}{dx^2}\Psi_n(x)+\left(gx^4+\frac{1}{x^2}\right)\Psi_n(x)=E_n\Psi_n(x),\qquad x\in(-10,10),\qquad\Psi(-10)=\Psi(10)=0$$ The boundary of $x$ is ...