# 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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### 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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### 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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### 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....
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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### 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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### 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 ...
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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### Eigenfunctions returned from NDEigensystem not in correct order

First I solved for the eigenfunctions and stored them as "funs": ...
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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 \... 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 ... 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. ... 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: ... 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: $$\Lambda=UHU^{-... 0answers 47 views ### Large difference between algebraic and numerical eigenvector system I'm working on a general procedure where I need to obtain the eigen-decomposition of a matrix. I noticed the following funny difference, though. When I use ... 1answer 140 views ### Sensitivity analysis of parameter on eigenvalues of predator-prey model I am trying to do a sensitivity analysis of the parameter g on the eigenvalues of this simple predator-prey Lotka Volterra model. I know that this code is entirely ... 1answer 24 views ### Error: Root::npoly: not a polynomial in #1 [closed] I have a 45\times 45 matrix H and its elements depend on Ca. I want to find its eigenvalues (which will also depend on Ca). I do this using: ... 1answer 51 views ### Plotting the Eigenvectors with respect to a parameter I have a matrix M(\lambda) of the form given below with a parameter \lambda. I would like to plot the quantity$$\langle\phi_{i}|Q|\phi_{i}\rangle$$for every Eigenvectors corresponding to ... 0answers 36 views ### Parallel Matrix Manipulation: find eigenvalues and construct list I'm having some trouble with the Parallel commands in Mathematica 12.1: I need to construct a table where its entries are {M, Eigenvalues of X[M]}, where X is a square matrix of dimension N with N big ... 1answer 60 views ### Using/ Extracting data from Interpolating Functions returned from NDEigensystem I am relatively new to Mathematica and have been trying to use the NDEigensystem command to work with some quantum systems. I am able to get the accurate energy eigenvalues but am having problems with ... 1answer 155 views ### Fast method to calculating signature of a matrix For calculation of the topological properties of a hamiltonian, sometimes we need the signature of that matrix. This means we only need number of positive eigenvalues. One simple way is to first ... 0answers 34 views ### Difference in computation speed of Eigensystem not to expectation for ParallelTable and Table I was trying to compute the time it takes for Eigensystem to evaluate while being inside a ParallelTable, as it is well-known LAPACK subroutine has an inbuilt Parallelization to it. And the difference ... 2answers 296 views ### Solving a biharmonic eigenvalue Problem I am interested in solving the following biharmonic eigenvalue problem.$$\begin{array}{cccc} & \Delta ^2 \Psi (x,y) = \lambda \Psi (x,y), & - \frac{\pi}{2} \le x \le \frac{\pi}{2} & -\... 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, ... 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-... 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 ... 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 ... 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 $$\rho =\left( \begin{array}{cccc} G_+ & k & k & G_- \\ k & L_+ & L_- & k \\ k & L_- & ... 0answers 44 views ### Eigenvectors for two very close matrices [closed] I have two matrices. ... 3answers 159 views ### Numerical eigenvalues of the problem I have this equations with condition 0 <= x <= 1: ... 5answers 510 views ### NDEigenvalues vs. FindRoot for finding the eigenvalues of Airy equation? Say I am trying to find the first 5 eigenvalues of the differential equation f''(x)=\lambda x f(x), on the interval [-1,0], with boundary conditions f(-1)=f(0)=0. I will try to do this 3 ways, ... 1answer 38 views ### Find the eigenvalues of 3-coupled equations matrix I'm trying to solve and and get the Eigenvalues (Natural frequencies later) of the matrix 3x3 for 3 Galerkin equation like in the pictures,,, where I solved them with one mode easily but with these ... 1answer 78 views ### Finding an eigenvector for a specific eigenvalue of a symbolic matrix The relevant matrix is$$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 &... 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. ... 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 ... 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 ... 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): $$\lambda_h \frac{\partial^2 \theta_w}{\partial x^2} + \lambda_c V \frac{\partial^2 ... 0answers 112 views ### Differing behavior of Eigenvalues and Eigensystem With the update to v12.0, I seem to be getting different behavior of eigenvalues returned by Eigenvalues and Eigensystem (oddly, ... 1answer 94 views ### Solving \det{(A+\epsilon B)}=0 for large, symmetric and dense A and B In an algorithm I am writing, I need to solve the equation$$ \det{(A+\epsilon B)} = 0,$$for the smallest value of$\epsilon$, given large ($n$x$n$ideally up to 150x150), dense and symmetric A ... 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 ...
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 ...