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Questions tagged [eigenvalues]

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Finding eigenvalues of the Laplacian on solenoidal (divergence-free) vector fields

In Mathematica it is easy to find eigenvalues of the Laplacian in simple cases. For example, on $\Omega\in \mathbb{R}^2$: ...
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0answers
33 views

Trying to extract the Eigen values and Eigen vector of a matrix

I have a Matrix A, which is a function of ω. I wanted to find the eigenvalues and eigenvectors of this matrix, how to do it. I have used the EigenSystem function ...
2
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2answers
112 views

Finding eigenvectors of a differential operator

How can I find the eigenvalues and eigenvectors(numerically) of the below matrix equation: $ \qquad \hat{A}\left({\begin{array}{c} y_1(x,\theta)\\ y_2(x,\theta) \\ \end{array} } \right)= ...
3
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2answers
54 views

Checking NDEigensystem Results

I'm looking to verify the output of a call to NDEigensystem. I'm doing this by plotting the operator acting on the Interpolating Function outputs versus the ...
2
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0answers
46 views

Block diagonalizing a complex anti-symmetric matrix

I am going to evaluate the block diagonal form of few skew-matrices. When matrix elements are real I can simply follow the approach suggested in this thread which I have implemented that as ...
0
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2answers
52 views

Trying to to replace Root expressions from the output of Eigenvalues by the explicit forms

When I calculate the eigenvalues of the following matrix (H) by using Eigenvalues, I get complex expressions with ...
2
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0answers
94 views

Why doesn't NDEigenSystem give smooth eigenfunctions? [closed]

I'm looking for smooth solutions of the 1D Helmholtz equation $\left[\frac{d^{2}}{dx^{2}}+k_{0}^{2}\epsilon(x)\right]\phi=0$ with homogeneous Dirichlet boundary conditions, where the permittivity $\...
4
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3answers
187 views

Eigenvectors in the limit $ \mu\rightarrow 0 $ are not the same as eigenvectors when setting $ \mu=0 $ from the beginning

I would like to find the eigenvectors of a matrix and see what the eigenvectors look like in the limit of $ \mu\rightarrow 0 $: ...
0
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1answer
49 views

Remove +0Is from Root function

I'm trying to find the zeros of the eigenvalues (functions of $k_x$) of a self-adjoint $4\times4$ matrix H: ...
3
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1answer
47 views

Trace change of one single value in a list

I have a list of eigenvalues, say: list1 = {10., 9., 9., 8.5, 7.5, 6.5, 6.1, 5.6, 4.5, 4., 4., 3.8, 3., 3., 1., 1., 1., 0.8, 0.5, 0.5} After slightly modifying ...
3
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1answer
86 views

Problem with complex eigenvalues in periodic Sturm-Liouville problem

I'm having trouble using NDEigenvalues to obtain the first few eigenvalues for a differential operator on the circle of radius one-half. $\qquad Lf(x) = f''(x)+ (-...
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0answers
32 views

Getting a non zero determinant of matrix R, when the Rank of R is not equal to Dimension of R

I have a square matrix whose dimensions is 9 cross 9, when I extract the rank of the matrix R, I am getting rank as 6. I have constructed R matrix by minimizing the Lagrangian Lg with respect to a[1].....
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24 views

Sequential production of Eigenvectors?

I have to deal with very large matrices in Mathematica (dimensions $10^4\times10^4$ at least). Obtaining the eigenvalues of these matrices is not so difficult since, it is not memory intensive or ...
4
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1answer
64 views

find a maximum parameter for a range of target eigenvalues as a function of matrix dimension

I have a symbolic tridiagonal matrix of this form ...
4
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2answers
915 views

Two matrices that are not similar have (almost) same eigenvalues [closed]

I have two matrices $$ A=\begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix} \quad \text{ and } \quad B=\begin{pmatrix} d & e & f \\ d & e &...
0
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1answer
88 views

How can I get the Eigen system of a certain matrix? [closed]

How can I get Eigen system of c, where c = a - iota * b? Please help me to find the Eigen system in a nice form. ...
3
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0answers
60 views

Derivative of eigenvalues

I work with 4x4 Hermitian matrices (r). I want to calculate a derivative of a function f[t,r] (ff[t_,r_]=1/2*D[f[t,r],t]), where the function f depends on the absolute value of the eigenvalues of r. ...
3
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2answers
755 views

Problem with Eigenvectors

When I want to calculate eigenvectors of the following matrix in Mathematica the only answer it gives me is zero vector, anybody knows how to fix this? here's my matrix : \begin{equation} X=\left(\...
5
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2answers
113 views

How to show just one function from a stored plot?

Q: Is there a general way to remove particular functions from a previously stored call to a plot function? Here is a specific example: ...
8
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0answers
269 views

DEigenvalues and NDEigenvalues return different values

In the following example, DEigenvalues and NDEigenvalues return different results despite having identical arguments. Does anyone know why? (I use Mathematica 11.3) ...
7
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1answer
128 views

How to solve this 1st-order linear ODE system with a few discrete eigenvalues?

I am trying to solve the eigensystem of a 1st-order linear ODE system in the region $(-\infty,\infty)$ and with Dirichlet boundary condition at the infinities $$ -i\partial_xu(x)+f^*(x)v(x)=\lambda u(...
0
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0answers
48 views

How to draw mode vectors of two degrees of freedom

Here is two degrees of freedom system. *And the mode vectors of this system is ({{1, 1},{1, -1}}) *And the mode shape will be expressed like this... And the ...
0
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0answers
122 views

Finding eigenvalues of a differential operator

I am trying to get the eigenvalues of the following differential operator $$L\psi(r) = -f \partial_r (f \partial_r \psi(r)) + V \psi(r)$$ which must satisfy (obviously) $$L \psi(r) = \omega^2 \psi(...
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0answers
37 views

Some issues with DEingesystem

I would like to solve (get its eigenvalues/vectors) the Sturm-Liouville problem, for the following differential operator: $L =\partial_{r} \partial_{r} \psi(r)$. Also, I would like to impose the ...
0
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0answers
51 views

Eigenvectors of Hermitian matrices [duplicate]

I asked a similar question in the physics stack exchange, but realized my question is probably more suited here. For any Hermitian matrix $H = H^{\dagger}$ we can write $H = P DP^{\dagger}$ where $P$ ...
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0answers
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Ordering of Eigenvectors [duplicate]

I am interested in computing the derivatives of the eigenvalues of a certain $n\times n$ Hermitian matrix $M(t)$. I know I can do this easily since I know the exact expression for $\dot{M}$, and the ...
4
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2answers
205 views

Help with coding a matrix

I have a $n \times n$ matrix $A$ with a full set of eigenvalues $\lambda$ including repetitions. I want to create the following $i \times i$ matrix: $$\left(\sum_{a=2}^i (a-1) |a-1⟩⟨a| \right) + \...
1
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1answer
142 views

Eigenvalue problem

my question is about solving an eigenvalue problem of the Helmholtz equation using sinc approximation $\nabla^2E + V (x) = \lambda E$ and $V(x)= X^2 / 2$ I have a problem in calculating the ...
0
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2answers
76 views

How to get eigenvectors of a 4x4 matrix? [closed]

MatrixForm[m = {{2, 9, 0}, {3, 8, 9}, {3, 9, 1}}] Eigensystem[m] I am facing problem in finding eigenvectors using ...
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0answers
18 views

Solve, store, and access eigenvalues and eigenstates of M[x,y], for various points {x,y}

I'm interested in solving a position dependent eigenvalue problem for matrix M[x,y], where {x,y} is some discretized set of points. I may need to access the eigenstates and eigenvalues multiple times ...
5
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2answers
149 views

Lowest Magnitude Eigenvalues of Large Sparse Matrices

I am trying to find the first three lowest eigenvalues of large sparse matrices of size range $10^3 - 10^5$. The matrices depend on some parameter $x$, so I first construct the matrices and then use ...
7
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3answers
554 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 ...
0
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1answer
53 views

Time used by Mathematica to calculate tridiagonal matrix

I have a question. I need to find the eigenvalues and eigenvectors of a tridiagonal matrix of size NxN. Can you tell me how much time does Mathematica need to do that in minutes? for Size N ...
5
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1answer
70 views

How to change the default normalization for NDEigensystem?

I'm currently using NDEigensystem to solve a PDE that describes a particle travelling on a hyperbolic (negatively curved) surface. However, the eigenfunctions that are returned by NDEigensystem are ...
5
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1answer
575 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 ...
3
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1answer
72 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. ...
36
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2answers
888 views

Eigenvalues broken in Version 12.0

Bug introduced in 12.0. The following code calculates the eigenvalues of a certain complex matrix, which come in pairs of opposite complex numbers. Therefore one can check whether the sum of all ...
0
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1answer
101 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
135 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 ...
2
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1answer
98 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
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1answer
87 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
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0answers
85 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
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2answers
79 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
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1answer
46 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
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1answer
97 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
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1answer
88 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 ...
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2answers
146 views

Eigen value solution of coupled ODEs

I want an eigen value solution of following coupled ODEs: But the code showing errors. ...
2
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1answer
67 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
64 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
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2answers
358 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 ...