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Questions tagged [eigenvalues]

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5
votes
1answer
101 views

How to plot the eigenvalues of a parametric matrix efficiently?

I was wondering how can I set the variable type of matrix elements to be real. The problem is, I creat a variable-dependent matrix as follows and I get the eigenvalues now I want to plot the ...
1
vote
0answers
18 views

How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?

Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows. ...
20
votes
2answers
247 views

Eigenvalues broken in Version 12.0

The following code calculates the eigenvalues of a certain complex matrix, which come in pairs of opposite complex numbers. The code plots the real part of adding each pair. So the correct plot should ...
0
votes
1answer
54 views

Using multiple boundary conditions with NDEigensystem

I'm quite new to Mathematica and to Stack Exchange so I apologise if this question has already been answered. I've recently been trying to solve a partial differential equation to find the ...
5
votes
1answer
127 views

Speed up selecting positive eigenvalues repeatedly

I have a smallish (e.g. 2x2 or 4x4, but ideally up to 10x10) non-symmetric square matrix $\mathbf{A}(x)$. I need to define a function $f(x)$ which is the sum of the eigenvalues with positive real part ...
0
votes
0answers
31 views

Root (#1^3 …) How exploit the result of Matrix Eigenvalues [closed]

I try to determine the Eigenvalues of matrix[4x4] (algebraic results) but I don't understand the result. How exploit the result with #1^3 ? I would like find a algebraic result for each eigenvalues. ...
2
votes
1answer
55 views

Using NDEigensystem to find 100 eigenvalues

I'm using "NDEigensystem" to calculate a Sturm-Liouville problem, for which the first 100 eigenvalues are needed. The code is like this: ...
1
vote
1answer
41 views

Why am I getting incorrect Eigenvectors for my matrix? [closed]

When i try and compute the Eigensystem using Mathematica i am getting negative values for my Eigenvector, but my Eigenvalues are correct but my Eigenvectors are incorrect and i do know why is that? \...
1
vote
0answers
72 views

Problems with the eigenvalues calculated using NDEigenvalue

I'm trying to solve a Sturm-Liouville problem like $\qquad -\psi''(z)+(\frac{1}{z}+2\,z)\psi'(z)=\lambda\,\psi(z)$ using NDEigensystem in order to learn how to ...
3
votes
2answers
67 views

Solution to eigenvalue BVP using NDEigensystem to high precision

I'm trying to solve linear (non-self-adjoint) boundary-value problems to as high precision as possible (optimally 1e-15). For example, the below code solves for the first 5 eigenvalues of the harmonic ...
0
votes
1answer
37 views

Simplifying an expression involving a matrix and functions of it

I have implemented the following two matrices in Mathematica in order to compute s, but I don't know how I can further simplify the resulting expressions, e.g., ...
2
votes
1answer
75 views

Eigenvalue dependent boundary conditions- mathematica

I am dealing with an eigenvalue problem whose boundary conditions are also eigenvalue dependent. Could anyone please comment whether Mathematica can numerically solve such a problem? For boundary ...
0
votes
1answer
70 views

Obtaining eigenvectors without using Eigenvectors

Introduction I am trying to obtain the eigenvectors of a unitary matrix $M(k)$ which depends on a parameter k. This matrix $M(k)$ has dimension 6, and while for general matrices of dimension 6 it's ...
1
vote
2answers
129 views

Eigen value solution of coupled ODEs

I want an eigen value solution of following coupled ODEs: But the code showing errors. ...
2
votes
1answer
54 views

Efficient computation of matrices involving large sums of KroneckerDelta's

I was wondering if one could benefit from Mathematica's rich linear algebra methods for diagonalizing 2nd rank tensors. Namely, in the context of systems (fluids) comprised of capsule-like particles, ...
3
votes
1answer
59 views

Evaluating Hough functions by using NDEigensystem on the Laplace tidal equation

Currently I am looking into the use of Mathematica to solve the classical tidal equation of M. Laplace: $$\mathcal{F}\Theta+\gamma\Theta=0$$ whose eigenfunctions $\Theta$ are the Hough functions. ...
6
votes
2answers
323 views

Using NDEigensystem to solve the Mathieu equation

To be able to apply the differential equation capabilities of Mathematica to my graduate thesis, I am trying to apply NDEigensystem to an eigenproblem whose solution I know, but I am having some ...
0
votes
0answers
40 views

Why is this iterative process with matrix calculation so slow?

I am trying something similar to the following code with Ntime as large as 100 or so. Now it's very slow as shown by the Ntime=3 ...
5
votes
2answers
881 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. ...
3
votes
0answers
45 views

Interface points of NDEigensystem

When solving an eigenvalue problem with "NDEigensystem", e.g. a 1D Eigenvalue problem with the interval composed of different materials, which should be solved by the pure numerical method such as FEM,...
2
votes
1answer
64 views

Meshing control of NDEigensystem

I have to solve an Eigenvalue problem originating from the Electrodynamics. It is a 2-D problem with a rectangular region. More specifically, there is a hole on a rectangle made by magnetic material. ...
1
vote
1answer
30 views

Defining a function that outputs a matrix, and later finding its eigenvalues

I am trying to do the following: I have a simple 2x2 matrix that depends on three parameters (physically -- momentum coordinates kx, ky, kz). Then I want to replace each of these parameters by a ...
3
votes
2answers
88 views

Efficiently find all values of parameter such that any of the eigenvalues of a matrix is equal to 1

I wish to find all values for a parameter such that my matrix has an eigenvalue of 1. Here is an example 16-by-16 matrix with elements depending on the parameter x ...
1
vote
1answer
79 views

How to write the equation into matrix form [closed]

$[(a+k_i)^2+(b+k_j)^2]X_{i,j}-\sum_{m,n}V_{m,n}X_{i-m,j-n}=\mu X_{i,j}$. where $-N\le i,j\le N$ Here we can set $ N=10,a =1, b=1$ and $V_{m,n}$ is the matrix element of $V$. Once I write the ...
4
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0answers
64 views

Orthogonal matrix decomposition of symmetric matrix?

If matrix mat is symmetric, we should be able to decompose it into eigenvalue matrix matJ and orthogonal matrix ...
0
votes
0answers
68 views

Diverging solution to radial equation

I want to solve a seemingly simple eigenvalue problem. I have a fixed set of boundary conditions given and want to change the complex parameter omega in to minimize exponentially falling solutions for ...
2
votes
2answers
90 views

Unable to evaluate Eigenvalues and Eigenvectors for a matrix (2)

I have posted a similar question last year pertaining to this issue. Here's a link to my post together with the solution given: Unable to evaluate Eigenvalues and Eigenvectors for a matrix I have ...
2
votes
1answer
62 views

How can I tell if a matrix is ill-conditioned or Singular by using the Eigensystem function(or LUDecomposition)?

I'm using the Eigensystem function, and I'm trying figure out whether or not it is singular or ill-conditioned. I'm using the function as so: ...
1
vote
2answers
57 views

Table Command with multiple Variables

I am new to Mathematica, so I'm not sure about the ins and outs of what's possible and what is not. I am trying to view the eigenvalues of multiple matrices at once. In particular, this matrix: $$\...
0
votes
1answer
44 views

Creating functions from a eigenvalues output [closed]

I need to create a function with the Eigenvalues output. The problem in question is that I need to manipulate variables from the eigenvalues and then plotting them. ...
2
votes
3answers
62 views

Plotting Solve output automatically

I am trying to solve a characteristic polynomial and plotting its output. The problem is that I do not know how to take the output automatically. My current code is ...
2
votes
1answer
34 views

Eigenvalue decomposition of a density matrix not reproducing original density matrix

A density matrix $\rho$ in quantum mechanics is defined as any self adjoint and positive semidefinite matrix with a trace or 1. It can be expanded into sets of pure states such that $\rho=\sum_{i}p_{...
0
votes
1answer
53 views

Strange answer for Eigenvalues of a 4x4 matrix [duplicate]

I am getting these strange eigenvalues of this simple looking 4-dimensional matrix: ...
2
votes
1answer
36 views

Performance Tuning: Construction of Matrix with Summations

I am trying to solve an eigenvalue problem of a large matrix. The issue is that it takes too much time to construct this large matrix. This is the code that I built: ...
1
vote
2answers
66 views

Eigenvalues error: “The method ”Banded“ accepts only sparse matrices with elements that are machine-real or machine-complex numbers”

I'm having one issue with the Eigenvalues function in some code priorly discussed here. There the example is tridiagonal, but here, let us consider this simple ...
1
vote
0answers
42 views

Fast Plot3D, failing NIntegrate, and reckless surgery

I have a square matrix, m which depends on kx and ky. It isn't Hermitian, but it does have ...
2
votes
1answer
102 views

What am I doing wrong when trying to plot this function?

I'm trying to reproduce the computations of this paper and I'm running into some troubles because I'm rather new to Mathematica. In the paper's page 4, in figure 2 the authors show a plot of a ...
6
votes
0answers
59 views

Where is the mistake in computing the particular eigenvector of the following DFT Matrix?

I have the following matrix (the DFT Matrix for N = 3) $$W = \frac{1}{\sqrt{3}}\begin{pmatrix} 1 & 1 & 1 \\ 1 & e^{-\frac{i 2 \pi}{3} } & e^{\frac{i 2 \pi}{3} } \\ 1 & e^{\frac{...
4
votes
1answer
107 views

Numerically computing the eigenvalues of an infinite-dimensional tridiagonal matrix

I have one infinite dimensional tridiagonal matrix whose eigenvalues I have to compute. How can that be done numerically using Mathematica? Let me expose the concrete case I want to do it. I shall ...
3
votes
1answer
284 views

1st-order linear ODE system gives inaccurate/biased solutions

Consider an ODE eigensystem $$ t(y+\frac{1}{s})a(y)+[(q+\frac{1}{2}+\frac{s}{2}y)+s(y\partial_y+\frac{1}{2})]b(y)=\lambda a(y)\\ t(y+\frac{1}{s})b(y)+[(q+\frac{1}{2}+\frac{s}{2}y)-s(y\partial_y+\frac{...
2
votes
1answer
115 views

How to solve this 2nd-order ODE with quadratic coefficients?

Consider an ODE eigensystem $$ \begin{bmatrix} 0 & d_1-\mathrm id_2 \\ d_1+\mathrm id_2 & 0 \end{bmatrix} \begin{bmatrix} a(y) \\ b(y) \end{bmatrix} = \lambda \begin{bmatrix} a(y) \\ b(...
0
votes
0answers
44 views

Plot Eigenvalue Data

`kmin = 0; (* min wave number *) kmax = 5; (* max wave number *) nopoints = 51; step = (kmax - kmin)/(nopoints - 1); ktable = Table[k, {k, kmin, kmax, step}];` I ...
3
votes
2answers
181 views

Eigen values of a third order linear homogenous ODE

From a system of PDEs where i used the following ansatz: $$\theta_w(x,y) = e^{-\beta_h x} f(x) e^{-\beta_c y} g(y)$$. $F(x) := \int f(x) \, \mathrm{d}x$ and $G(y) := \int g(y) \, \mathrm{d}y$ So, $$\...
3
votes
3answers
141 views

Plotting eigenvalue function along a path with correct coloring

This question has multiple parts to it. The setup is that I have a matrix that is a function of two parameters a and b. I wish to plot the eigenvalues of this matrix along a general path in the a-b ...
1
vote
1answer
122 views

How Can We Solve The Eigenvalues of partial-integral equation?

Here, my problem is that $$ \left(\int_{-L_0}^{L_0} \left(\int_{-L_0}^{L_0}\mathrm e^{-(x-x_1)^2-(y-y_1)^2} ({\bf u_{\lambda}}(x_1, y_1) + {\bf v_{\lambda}}(x_1, y_1)) \, \mathrm dx_1\right) \, \...
9
votes
1answer
309 views

How to solve this 2nd-order ODE with singularity?

I tried solving the eigenvalue problem of a 2nd-order ODE $$[b^2(k-2)^2y^2-2b(k-2)(1+2ky)+4k^2+b^2(k-2)3y]f(y) \\- 3b(3by-2)f'(y)\\-(3by-2)^2f''(y)=\lambda f(y)$$ with ...
-1
votes
1answer
131 views

How to compute eigenvalues of a large symbolic matrix?

I am trying to find eigenvalues for a big matrix having symbolic elements. Basically I am trying to find values of lambda for which matrix $(A-\lambda)$ is singular. For small matrices, we generally ...
0
votes
0answers
50 views

JordanDecomposition: Error Mesage eivn

I want to calculate the JordanDecomposition of the follwoing matrix: That is ...
4
votes
1answer
226 views

Solving the eigenvalue problem for a double well potential using a 1D particle in a box as a basis set

My first question is how would I go about getting the 1D particle in a box eigenfunctions using matrix techniques and how would I use the particle in a box eigenfunctions as a basis set for the ...