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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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]...
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5 votes
3 answers
291 views

Linear ODEs with NDSolve

I am trying to solve some first order linear odes. My code is below: ...
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0 votes
0 answers
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 ...
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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 ...
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0 answers
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 ...
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2 votes
1 answer
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: ...
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2 votes
1 answer
102 views

NDEigensystem returns reversed list of eigenfuctions

I'm considering the two coupled linear differential operators ...
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0 votes
0 answers
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 <...
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2 votes
2 answers
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 ...
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1 vote
0 answers
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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 ...
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4 votes
1 answer
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 ...
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1 vote
0 answers
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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. ...
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3 votes
1 answer
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] ...
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2 votes
2 answers
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 ...
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1 vote
0 answers
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 ...
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4 votes
0 answers
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 ...
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2 votes
1 answer
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 ...
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0 answers
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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 ...
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3 votes
1 answer
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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 ...
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8 votes
1 answer
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-...
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1 vote
1 answer
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? ...
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0 answers
133 views

Could all eigenvalues of this matrix be positive?

I have the following list $\beta$ with 5 equations ...
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1 answer
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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. ...
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3 votes
2 answers
164 views

Solve quantum mechanics 1D box using NDEigensystem

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5 votes
0 answers
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 ...
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3 votes
3 answers
227 views

Eigenvalue problem with NDSolve

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

How to integrate product of eigenfuctions found using NDEigensystem?

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4 votes
1 answer
77 views

NIntegrate over eigenfunctions found using NDEigensystem

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  • 449
0 votes
1 answer
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 ...
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2 votes
1 answer
108 views

Solving boundary value problem with coupled odes at interface

I am trying to get the eigenvalues of the following differential system ...
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2 votes
1 answer
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 ...
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4 votes
1 answer
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: <...
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1 vote
1 answer
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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 ...
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19 votes
2 answers
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, ...
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2 votes
2 answers
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 ...
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13 votes
3 answers
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] ...
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1 vote
0 answers
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'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 ...
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1 vote
1 answer
68 views

Obtaining more values from `NDEigenvalues`

When I run this code ...
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0 votes
1 answer
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 $$ H_{nm}=\delta_{nm}\left (n^2+v[b_1-b_0-h(2m,b_0,b_1)]\right) \\ +v(1-\delta_{nm})\left (h(n-m,b_0,b_1)-h(n+m,b_0,b_1)\right) $$ ...
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0 votes
1 answer
80 views

Problem with the plots of eigenvalues of the Matrix

I am trying to plot the eigenvalues of the following matrix ...
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2 votes
1 answer
34 views

Using Maximize function with UnitaryMatrixQ constraint

Define a function ...
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2 votes
0 answers
52 views

NDEigensystem potential with a singularity

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 ...
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2 votes
1 answer
82 views

Custom Normalization for NDEigensystem

I am trying to solve the Laplace equation in polar coordinates $$-\left(\frac{\partial^2\psi_n(r,\theta)}{\partial r^2}+\frac{1}{r}\frac{\partial\psi_n(r,\theta)}{\partial r}+\frac{1}{r^2}\frac{\...
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  • 341
2 votes
1 answer
147 views

define edge set of a graph

I want to define a graph in Mathematica which its vertex set is cartesian product of two sets. I define the vertex set by Tuple[] but two vertices are adjacent if and only if the intersection of the ...
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1 vote
1 answer
81 views

Find interval/range of certain coefficients to prove conditions of eigenvalues

I have seen similar questions to the one I am posting here, but I haven't been able to execute it on Mathematica. I would request some help with the following: I have the following matrix: ...
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3 votes
1 answer
159 views

Eigenvalues of $i x^3$ potential

There is a famous paper by Carl Bender et al., where they investigated a class of non-Hermitian potentials and showed their spectrum is entirely real. One such a case is $i x^3$ potential. I would ...
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0 votes
0 answers
46 views

Indexing of NDEigensystem Result on a Cluster

I am trying to run on a cluster (where the version 11 of Mathematica is available) a code involving the following calculation: ...
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0 votes
0 answers
118 views

How to implement the symplectic transformation in Mathematica?

Consider a $4\times 4$ matrix $A$, which can be diagonalized by a symplectic matrix S such that $$A = SA_d S^T$$ where $A_d = \oplus_{k=1}^{2} a_k \mathbf{I}$ where $a_k$ is the $k$-th symplectic ...
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7 votes
0 answers
158 views

How to compute eigenvalues of linear function (not matrix)?

How to compute eigenvalues of a known linear function? In Julia, there is a package https://jutho.github.io/LinearMaps.jl/dev/ to compute the matrix representation of given function, then we can ...
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4 votes
0 answers
98 views

How to use NDEigenvalue to accurately estimate functional determinants?

Goal: Ultimately, I would like to find a trustworthy approximation for the ratio of the functional determinant of two differential operators using the formula $$ \frac{\text{Det}[\hat{D}_0]}{\text{Det}...
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