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
78 views

Solving Helmholtz equation in 3D for torus

How I can solve the Helmholtz equation in 3D for torus? According to the following post, I encounter an error when I run the program. Any help would be graet! Numerically solving Helmholtz equation in ...
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0answers
35 views

how can I correct this code? [duplicate]

I need to calculate matrix m1 according to following algorithm. Then, I have to put it in the differential equation. However, matrix m1 is complex and therefore the differential equation does not work....
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51 views

How can I correct this code to get an answer? [duplicate]

I need to calculate matrix m1 according to following algorithm. Then, I have to put it in the differential equation. However, matrix m1 is complex and therefore the differential equation does not work....
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0answers
65 views

How to solve the following equation numerically?

In the following code, if the matrix "n = (-I*(m1)) + (m2)" in the differential equation contains only the matrix "m1", I will get the answer, but if the matrix "n" is ...
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0answers
47 views

solving a 2D eigenvalue problem for a partial differential equation

I'm fairly new to Mathematica and I'm looking for a way to solve a partial differential equation subject to periodic boundary conditions. The form of the equation looks like this: $\frac{\partial^2}{\...
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2answers
61 views

Integrate over one variable of a 2D interpolating function returned from NDEigensystem

I'm trying to implement the answer for "Integrate only one variable of a 2D interpolating function" (https://mathematica.stackexchange.com/a/161962/73672) but for interpolating functions ...
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0answers
48 views

Strange behaviour of eigensystem

I encounter with really strange behavior in calculating the eigensystem of a hermitian matrix. I upload the matrix here. After loading it you can construct the main matrix as follows ...
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5answers
182 views

Simplifying away imaginary part

I'm solving the following eigensystem, and I get result which looks complex-valued. I expect the result to have 0 imaginary part, can anyone see a way to simplify it away? ...
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1answer
48 views

Generate constraints that ensure positive definiteness

What is a good way to generate algebraic constraints that ensure matrix be positive definite? Ideally, I'd be able to do something like below ...
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1answer
25 views

Problem for defining continously Eigenvectors from Kane and Mele model

The model is a simple eigenvalue problem. A matrix that depends on some parameters kx, ky, t, defined by: ...
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0answers
37 views

Determine a negative semidefinite 5*5 matrix

I'd like to find the real parameters $\left\{p,\alpha ,a_{24},c_3,c_7,c_9,c_{10}\right\}$ in $M$, which is a $5\times 5$ real symmetric matrix, such that $M$ is negative semidefinite. My code for $M$: ...
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1answer
52 views

Determine a positive semidefinite 5*5 matrix

I'd like to find the real parameters $\left\{a_{14},c_6,c_8,c_{10},c_{12},c_{13},c_{14},c_{15},\alpha \right\}$ in M, which is a $5\times 5$ real symmetric matrix, such that M is positive semidefinite....
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1answer
76 views

Different results in DEigensystem compared to NDEigensystem for Laplacian eigenvalue problem (-Δu=λu) on unit square

I want to calculate the solution to the Laplacian eigenvalue problem on the unit square with trivial Dirichlet boundary conditions: $$- \Delta u(x,y) = \lambda u(x,y) \text{ on } {[0,1]}^2$$ with $u(0,...
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1answer
205 views

Eigenvalues of 3D Laplacian on a spherical segment

To study the change in Laplacian eigenvalues on a spherical segment, I constructed a table of spherical segments using the code from here. I discretized the output using ...
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0answers
39 views

Effectivelly using Compile for calculate a Unitary transformation

I am new to Mathematica, and this is my first post, so if my question is not clear enough, I would be glad to read the comments and edit my question to add more information. The problem I need to ...
3
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1answer
154 views

Plotting Eigenvalues and severe Noise Problems

I am trying to plot Eigen values of my System Hamiltonian in Mathematica. This is generating very noisy plot. This is my code. ...
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1answer
59 views

Eigenfunctions returned from NDEigensystem not in correct order

First I solved for the eigenfunctions and stored them as "funs": ...
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2answers
441 views

How to collect eigenvectors corresponding to only positive eigenvalues?

Let us consider a matrix of order $n \times n$ with $n/2$ positive and $n/2$ negative eigenvalues. How to collect $n/2$ eigenvectors corresponding to positive eigenvalues in a matrix of order $n \...
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0answers
56 views

Removing Unwanted Eigenvalues, Twisted bilayer Graphene Hofstadter Butterfly

I am plotting eigen values of a matrix. I want to remove unwanted eigenvalues from the plot. For try run this is possible to manually remove these unwanted eigen values. But for actual run this is not ...
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2answers
932 views

Noise in Eigenvalues plot

I am trying to Plot Eigenvalues of a Hamiltonian, but I am getting noisy plot, which is incorrect. Here is the code. ...
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0answers
33 views

Mathematica precision on extensive eigenvalues calculations

Im trying to evaluate some dot products with eigenvectors and matrices using Mathematica. My problem is the following: To an given matrix 6x6: ...
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1answer
125 views

Why sometimes eigenvectors matrix cannot transform to initial matrix?

As we know, $$H=U^{-1}\Lambda U $$ where $\Lambda $ is the diagonal matrix and $H$ is the original matrix, $U$ is the eigenvector matrix. Also, we can restore the original matrix via: $$\Lambda=UHU^{-...
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0answers
47 views

Large difference between algebraic and numerical eigenvector system

I'm working on a general procedure where I need to obtain the eigen-decomposition of a matrix. I noticed the following funny difference, though. When I use ...
7
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1answer
140 views

Sensitivity analysis of parameter on eigenvalues of predator-prey model

I am trying to do a sensitivity analysis of the parameter g on the eigenvalues of this simple predator-prey Lotka Volterra model. I know that this code is entirely ...
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1answer
24 views

Error: Root::npoly: not a polynomial in #1 [closed]

I have a $45\times 45$ matrix $H$ and its elements depend on $Ca$. I want to find its eigenvalues (which will also depend on $Ca$). I do this using: ...
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1answer
51 views

Plotting the Eigenvectors with respect to a parameter

I have a matrix $M(\lambda)$ of the form given below with a parameter $\lambda$. I would like to plot the quantity $$\langle\phi_{i}|Q|\phi_{i}\rangle$$ for every Eigenvectors corresponding to ...
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0answers
36 views

Parallel Matrix Manipulation: find eigenvalues and construct list

I'm having some trouble with the Parallel commands in Mathematica 12.1: I need to construct a table where its entries are {M, Eigenvalues of X[M]}, where X is a square matrix of dimension N with N big ...
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1answer
60 views

Using/ Extracting data from Interpolating Functions returned from NDEigensystem

I am relatively new to Mathematica and have been trying to use the NDEigensystem command to work with some quantum systems. I am able to get the accurate energy eigenvalues but am having problems with ...
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1answer
155 views

Fast method to calculating signature of a matrix

For calculation of the topological properties of a hamiltonian, sometimes we need the signature of that matrix. This means we only need number of positive eigenvalues. One simple way is to first ...
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0answers
34 views

Difference in computation speed of Eigensystem not to expectation for ParallelTable and Table

I was trying to compute the time it takes for Eigensystem to evaluate while being inside a ParallelTable, as it is well-known LAPACK subroutine has an inbuilt Parallelization to it. And the difference ...
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2answers
296 views

Solving a biharmonic eigenvalue Problem

I am interested in solving the following biharmonic eigenvalue problem. $$\begin{array}{cccc} & \Delta ^2 \Psi (x,y) = \lambda \Psi (x,y), & - \frac{\pi}{2} \le x \le \frac{\pi}{2} & -\...
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1answer
39 views

DecompositionNDSolveValue analogue for NDEigenvalues

In FEMAddOns there is a function DecompositionNDSolveValue to solve stationary PDEs on a cluster. Is there a similar way to solve the eigenvalue problem for a system of ODEs in parallel kernels, ...
6
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1answer
128 views

Which methods are available for NDEigensystem?

I am trying to find out what methods/options are available for NDEigensystem and descriptions of their use. Perusing the help, online Q&As, Mathematica's in-...
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3answers
793 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 ...
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2answers
1k views

How do you find the eigenvalues of a PDE (Dynamic Euler-Bernoulli beam)?

I am continuing to work on the vibration of a beam modeled by the Euler-Bernoulli equation. I have had some good answers to simulating the motion which may be found here. Now I wish to calculate the ...
3
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1answer
73 views

If I have the eigenvalues, can I find the corresponding eigenvectors?

The eigenvectors ($\psi _i$) of the following matrix are rather complicated $$ \rho =\left( \begin{array}{cccc} G_+ & k & k & G_- \\ k & L_+ & L_- & k \\ k & L_- & ...
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3answers
159 views

Numerical eigenvalues of the problem

I have this equations with condition 0 <= x <= 1: ...
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5answers
510 views

NDEigenvalues vs. FindRoot for finding the eigenvalues of Airy equation?

Say I am trying to find the first 5 eigenvalues of the differential equation $f''(x)=\lambda x f(x)$, on the interval [-1,0], with boundary conditions $f(-1)=f(0)=0$. I will try to do this 3 ways, ...
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1answer
38 views

Find the eigenvalues of 3-coupled equations matrix

I'm trying to solve and and get the Eigenvalues (Natural frequencies later) of the matrix 3x3 for 3 Galerkin equation like in the pictures,,, where I solved them with one mode easily but with these ...
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1answer
78 views

Finding an eigenvector for a specific eigenvalue of a symbolic matrix

The relevant matrix is $$M=\left( \begin{matrix} p^3+\frac{1}{\sqrt{3}}p^8 & p^1-ip^2 & p^4-ip^5 \\ p^1 +i p^2 & -p^3 + \frac{1}{\sqrt{3}}p^8 & p^6-ip^7\\ p^4+i p^5 & p^6+i p^7 &...
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2answers
64 views

Undesired complex number in the square root

I am trying to solve the eigenvalues of a hamiltonian The code I used is typed below. ...
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0answers
92 views

Memory usage for smallest eigenvalues

I have a bunch of hermitian matrices which are huge (of order 2^17 x 2^17) but extremely sparse so that, when I build the matrices, the usage of RAM is low (say of order 1 GB or similar). The ...
10
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2answers
873 views

NDEigensystem cannot solve numerically the 3D Coulomb problem, while DSolve returns the right answer

After having derived by hand the eigenvalues and eigenfunctions for the 3D and 2D hydrogen atom, I want to solve the systems numerically using Mathematica. I need to do this because my next step is to ...
4
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1answer
268 views

A complicated boundary value problem leading to third order Eigen sytem [Help in continuing forward] [EDITED]

I have the following elliptic PDE (describing temperature in a plate, w in thermal contact with two fluids h and c): $$\lambda_h \frac{\partial^2 \theta_w}{\partial x^2} + \lambda_c V \frac{\partial^2 ...
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0answers
112 views

Differing behavior of Eigenvalues and Eigensystem

With the update to v12.0, I seem to be getting different behavior of eigenvalues returned by Eigenvalues and Eigensystem (oddly, ...
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1answer
94 views

Solving $\det{(A+\epsilon B)}=0$ for large, symmetric and dense $A$ and $B$

In an algorithm I am writing, I need to solve the equation $$ \det{(A+\epsilon B)} = 0, $$ for the smallest value of $\epsilon$, given large ($n$x$n$ ideally up to 150x150), dense and symmetric A ...
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1answer
144 views

Det, MatrixRank and Eigenvalues

I consider myself to be an inexperienced Mathematica user so maybe someone could point out what am I doing wrong. In short, here is what I want to get: suppose that there is a matrix of dimension $ N ...
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1answer
97 views

How to collect the negative eigenvalues of a matrix?

I want to plot Sum[E[i]] verseus t where E[i] are the negative eigenvalues of the matrix: <...
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1answer
249 views

Finding the orthogonal diagonalizing similarity of a symmetric matrix

I'm aware that there are some questions similar to this here, but none that could solve my problem. So, I have to diagonalize a symmetric symbolic matrix $m$ (to be seen below) and obtain the ...

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