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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49 views

How can I get rid of Abs?

In the following code, the functions WP[t] and WS[t] are real. Time also is a positive parameter. As you can see, MATHEMATICA enters Abs in the calculations. Including Abs only complicates the next ...
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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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1answer
116 views

Solving Helmholtz equation in 3D for torus

How I can solve the Helmholtz equation in 3D domain? According to the following post, I encounter an error when I run the program. Any help would be graet! Numerically solving Helmholtz equation in 3D ...
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67 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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58 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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51 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
184 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
50 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
77 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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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 ...
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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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2answers
64 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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57 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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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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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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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 ...
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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
61 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
157 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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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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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, ...
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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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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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44 views

Eigenvectors for two very close matrices [closed]

I have two matrices. ...
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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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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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0answers
113 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
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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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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0answers
62 views

Finding eigenvalues of a large ( >1000 x 1000) matrix accurately

I'm doing a spectral method-based eigenvalue problem where I create a matrix, A, of size (nr+1)(nz+1)(2nf+1) where nr,nz,nf are integers, composed of a diagonal of (2nf+1) submatrices of size (nr+1)*(...
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1answer
43 views

Strange numerical values of Eigenvectors

When I calculate Eigenvalues and Eigenvector by using: Eigensystem[{{3.8, 21, 21}, {0.3, 3.5, 2.5}, {-0.8, -6.2, -5.2}}] I get the following result: ...
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0answers
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What does Eigensystem::geinsl1 mean (a solution for the generalized eigenproblem may be incorrect)?

I'm trying to solve a generalized eigenvalue problem and ran across a warning Eigensystem::geinsl1: Warning: a solution for the generalized eigenproblem may be incorrect. Here's a minimal working ...
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0answers
86 views

How can I improve the speed of computing of numerical integration and eigenvalue?

First, let me explain what I am calculating. I have the following 2D-equation: $$ w(x,y) = \sum_{m}^{M}\sum_{n}^{N}A_{mn}\sin\left(\frac{2m\pi x}{a}\right)\sin\left(\frac{2n\pi y}{b}\right) $$ ...
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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 ...
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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
50 views

Help in modifying my code

In my code, I want to plot (Dis[t]). The problem is some functions containing in the code do not work well if there are variables in the form of symbols, such as "Sort" "NMaximize" functions. I want ...
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1answer
39 views

Mathematica outputs its input; Eigensystem [duplicate]

I am simply trying to find the eigenvalues of a symbolic matrix using Matematica, but it does not give me an answer; it just outputs its input. (u is a parameter) ...
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1answer
38 views

Find minimal recoding of the (symbolic) entries of an $8 \times 8$ matrix

I have the following $8 \times 8$ matrix ...
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1answer
71 views

Arnoldi method misses eigenvalues degeneracies for very sparse matrices

I am here to signal a problem very very similar to the one already discussed here Wrong eigenvalues from a sparse matrix In particular, I have a very sparse matrix and I am asking just few dominant ...
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0answers
47 views

Computing the first eigenfunction of the p-Laplacian in a real interval

How can I numerically compute the first (non-negative) eigenfunction $u$ of the $p$-Laplacian ($p>1$) in a bounded interval $(-a,a) \subset \mathbb R$ (up to positive multiplicative constant)? $$-\...
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0answers
30 views

Computing matrix eigenvalues with units

I apologize if this is a basic question or if I am not giving enough detail. I'm trying to solve for the eigenvalues of a matrix with matrix elements that have units. ...

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