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Questions tagged [eigenvalues]

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3
votes
1answer
59 views

Getting the overlap of NDEigenfunctions of different problems

I am solving a number of Schrödinger eigenvalue problems for an array of different potentials, and I would like to calculate, in a quick, efficient and natural way, the overlap between the different ...
0
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0answers
66 views

Testing a (numerical) matrix for positivity

I’ve been testing certain randomly-generated $6 \times 6$ symmetric (and also Hermitian) matrices ($H)$ for positive definiteness, using the command ($n$, of course, being a count variable), ...
0
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0answers
38 views

Eigenvectors calculation doesn't match from two identical results

I have a $3\times 3$ matrix, depending on a single parameter. My job is to find the eigenvectors for the matrix. I tried two ways, shown below ...
4
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0answers
268 views

Spectral problem for differential vector operator (calculation of EM field in a cavity)

I know that mathematica has a DEigensystem and NDEigensystem which allow one to find eigenfunction and ...
3
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1answer
166 views

Can NDEigensystem use arbitrary precision arithmetic?

Consider the following computation of an eigenfunction of 1D Laplacian on the interval of $[0,\pi]$: ...
22
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1answer
1k views

Eigenvalues broken in 11.2?

Bug introduced in 11.1.0 and fixed in 11.3.0 The code ...
16
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8answers
871 views

Tracking Eigenvalues Through a Crossing

Suppose I have a matrix which depends on some parameter. I want to compute the eigenvalues as a function of this parameter, and then plot them. For example, I may have a matrix representing the ...
1
vote
1answer
165 views

NDEigensystem in a complicated case

Apologies for a boring question. I am trying to modify the standard Mathematica example for my needs. The only differences in my case are: A more complicated potential (double-well, grows rapidly). ...
6
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1answer
438 views

NDSolve eigenvalue problem of bound state

I am trying to solve this eigenvalue problem: \begin{align} \mu \Psi(r) & = -\frac{1}{2}\left ( \Psi^{\prime \prime}(r) + \frac{2}{r} \Psi' (r)\right ) -4\pi \Psi(r) \int _0^\infty dr' r'^2 \frac{...
3
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2answers
310 views

Why ODE's naive finite difference matrix works well for different boundary conditions

We know finite difference method (FDM) can replace $y''(x)$ as $\frac{1}{h^2}[y(x+h)+y(x-h)-2y(x)]$ or so. The naive way to write down the matrix of the differential operator is like the following, ...
0
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0answers
53 views

plotting functions containing branch cuts and crossings

For Functions That Do Not Have Unique Values, mathematical chooses a specific value; when plotting, say, the eigenvalue of a matrix that has such branch cuts, if the eigenvalues do not cross each ...
7
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5answers
495 views

Spectral problem for differential operator

I want to find numerically eigenvalue and eigenfunctions some nontrivial differential operator. But I can not find, how to do it in Mathematica. For the sake of simplicity let us discuss the trivial ...
0
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1answer
300 views

Change of basis from one linear mapping to another [closed]

I have this PDE which looks like this $\frac{d\vec{x}}{dt}= A\vec{x}+B\vec{x}$ Where $A$ and $B$ are both $n\times n$ matrices, and $\vec{x}$ is a state vector. Without making this too complicated ...
17
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7answers
1k views

How to check if a vector is an eigenvector of a matrix using mathematica?

Here is a vector $$\begin{pmatrix}i\\7i\\-2\end{pmatrix}$$ Here is a matrix $$\begin{pmatrix}2& i&0\\-i&1&1\\0 &1&0\end{pmatrix}$$ Is there a simple way to determine ...
0
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1answer
138 views

No eigenvectors coming for a very simple* matrix

I have a question regarding the same as Problem with Eigenvectors when given a matrix containing approximate numbers and symbols and Why won't Mathematica obtain eigenvectors for this symmetric ...
0
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0answers
123 views

finding eigenenergy/eigenvector pairs

This is perhaps more of a mathematics question rather than a Mathematica one, but I am looking for an easy Mathematica solution. I have a real square matrix consisting of four smaller blocks $H = \...
5
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0answers
77 views

Bug for Cubics -> True in Eigenvalues?

Let's consider the simple code ...
4
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2answers
437 views

Eigenvalues and eigenvectors of tensors

I have a linear equation where the unknown is a matrix: $$\sum_{pq} T_{ijpq}X_{pq} = \lambda X_{ij}$$ This is an eigenvalue problem for the tensor $T_{ijpq}$. Mathematica ...
0
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0answers
81 views

How to solve the eigenvalue problem that arises in stability of flows

I am an undergraduate student and I want to know how to solve this hydrodynamic stability problem. I tried but all my efforts have failed. Your suggestions will help me a lot. The equations are <...
0
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0answers
31 views

Eigenvaules of a symbolic matrix [duplicate]

If I try to find the eigenvalues in following way, mathematica gives something else other than algebraic expression, how to obtain algebraic expression ??? Please suggest something . ...
3
votes
1answer
316 views

Eigenvalue/eigenvector reordering and/or renormalisation?

I have two functions $f(x,y),g(x,y)$ and a matrix $M=\begin{pmatrix}\frac{\partial f}{\partial x} & \frac{\partial f}{\partial y}\\\frac{\partial g}{\partial x} & \frac{\partial g}{\partial y}...
2
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2answers
304 views

Eigenvalues and plot are very slow

I'mt trying to find eigenvalues (and plot them) but the evaluation takes way too long. I don't think it supposed to be a complicated computations. What am I doing wrong? ...
8
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1answer
544 views

Finding Eigenvalues for a boundary value problem

I have a 10x10 linearized BVP which I can write as $$\mathbf{y}'(x) = \mathbf{A}(\omega) \mathbf{y}(x)$$ subject to boundary conditions $$\mathbf{B} \cdot \mathbf{y} = \mathbf{0}, \quad x=0 \\ \mathbf{...
0
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0answers
134 views

Eigenfunctions to a Sturm-Liouville problem

I am trying to find the first 5 eigensolutions to a Sturm-Liouville problem; I have tried the code; ...
5
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1answer
435 views

How to use DEigensystem with periodic boundary conditions on the derivative?

Since I found I can use DEigensystem to obtain eigenvalues and eigefunctions for differential operators, I am using it to verify solution to some of my HW's. In ...
0
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0answers
135 views

Eigenvalues of a symbolic 28×28 Hessian matrix

I have a little problem trying to calculate the eigenvalues of big symbolic (depending on $a$) Hessian matrices (28×28, 32×32 ...). I think I've understand, by reading other posts, that Mathematica ...
2
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0answers
81 views

DEigenvalues with Robin B.C. sign problem

To find eigenvalues for $y''=\lambda y$ with robin boundary conditions on one end, and Dirichlet on the other end, I am getting correct value when robin B.C. on the right side, but when I flip things, ...
0
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1answer
129 views

why is there a minus sign on DEigenvalues “operator” as compared to the ODE itself?

In Mathematica, to find the eigenvalues for the following differential equation \begin{align*} y''(x)+ \lambda y(x) &=0 \\ y(0) &=0\\ y(L) &=0 \end{align*} The syntax one ...
5
votes
1answer
240 views

How to specify both DirichletCondition and NeumannValue on DEigenvalues?

Ok, I give up :) I am trying to verify the eigenvalues for heat PDE in 1D, when left end has homogeneous DirichletCondition but the right end is insulated, so it ...
2
votes
2answers
350 views

Problem with NDEigensystem

Consider the Sturm-Liouville problem $$y''(x) + \lambda x^2 y=0, \ y(0)=0,\ y(1)=0$$ The analytical solution is given by $$\lambda_n=4\alpha_n^2, \ y_n(x)=\sqrt{x}J_\frac14(\alpha_nx^2)$$ ...
3
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2answers
281 views

Using NDEigensystem to solve coupled eigenvalue problem

I want to find the Eigenvalues and Eigenfunctions for the following Eigenvalue problem I tried to solve this numerically ...
0
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1answer
137 views

How to solve the following system with NDSolve and FindRoot? Please address

Consider the following coupled systems of equations $f′′− k^2 f=k\, \mathbf{Ra}$ and $g′′− k^2 g=k\,f$ , where $f$ and $g$ are functions of $z$. The boundary conditions for the problem are $f=0$ and ...
5
votes
2answers
189 views

Checking if a symbolic symmetrical Matrix is negative definite

I have the following problem finding the value ranges for the parameters of a symbolic symmetrical matrix in order to make it negative definite: The matrix I'm talking about looks as follows ...
3
votes
0answers
114 views

NDEigenvalues and poles in a 2D Coulomb problem [closed]

I am trying to solve a hybrid Dirac/Schrodinger problem in 2D with a Coulomb potential. I am aware of the excellent post on the 2D Coulomb problem, but my problem lacks cylindrical symmetry so I can'...
4
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1answer
153 views

NDEigenvalues syntax

The internal documentation on NDEigenvalues is a bit unclear. I want to solve two coupled eigenvalue equations in 2D for two coupled eigenfunctions. The problem is of the form: ...
0
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0answers
141 views

Find Eigenvalues close to a Target for a Generalised Eigenvalue problem of the type Ax=λBx with A and B very sparse

So I have been using Mathematica as a tool to discretise large linear systems of PDEs and cast them as algebraic eigenvalue problems involving very large sparse matrices. These are usually complex and ...
2
votes
1answer
126 views

The algebraic solution and numerical solutions for eigenvectors are different. Why?

I find that the algebraic solution for the Eigenvectors of a 3x3 matrix is not correct when compared to the numerical solution. I don't see why ? ...
2
votes
2answers
285 views

Obtain the largest positive eigenvalue (with its eigenvector)? [duplicate]

Eigenvalues[M,1] can be used to return the largest eigenvalue in absolute value. Is there a simple way to obtain the largest positive eigenvalue instead, as well as ...
0
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0answers
381 views

How to compute the eigenvalue of a matrix over a finite field

How to compute the eigenvalue of a matrix over a finite field? I would like to compute the eigenvalues of the following matrix over $\mathbb F_5$. ...
2
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0answers
127 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} &...
2
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0answers
72 views

Eigenvector matrix of a real positive matrix to be from $SO(n)$. How?

Suppose I have a positive real matrix of dimension $n$ and as such there exists a diagonalizing (rotation) matrix that belongs to $SO(n)$. How do I force Eigensystem...
11
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0answers
661 views

What algorithm is Mathematica using to find the smallest eigenvalue so quickly?

My question is what kind of black magic is Mathematica doing to obtain the correct answer so quickly compared to other programming languages? Details: I've written a Mathematica notebook to find the ...
9
votes
1answer
275 views

Gaining precision/accuracy with NDEigenvalues

See further down for an important note Background I study (one component of) the semi-classical Pauli operator, $$ P_h=-h^2\Delta+ih(-y,x)\cdot\nabla+\frac{x^2+y^2}{4}-h. $$ For this particular ...
-3
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1answer
568 views

How can I plot eigenvalues?

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0
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1answer
261 views

Finding eigenvectors with given set of eigenvalues [duplicate]

I have a matrix whose eigenvalues I was trying calculate. Mathematica miserably failed in calculating the eigenvalues. So, I calculated them manually. But can I use it to find eigenvalues, atleast. ...
1
vote
1answer
83 views

Eigenvalues of a Matrix and RegionPlot

So, this is my problem. I have a 15 x 15 matrix with 7 parameters. I'm assigning numerical values to 5 of the parameters. Then, I do something like: ...
1
vote
1answer
166 views

Small positive eigenvalues found for a negative definite matrix

I have encountered a problem with Mathematica that I really don't know how to solve. I'm sorry if I am going to be very verbose but I need it to explain the problem properly (and also make the code I'...
2
votes
2answers
284 views

Finding only real eigenvectors of complex matrix

I'd like to compute the kernel of a complex matrix $M$, but only allow for real solutions $x$ of the matrix equation $M\cdot x=0$. Of course just kicking out the vectors in ...
13
votes
1answer
247 views

Specifying initial vector for finding Eigenvectors using Arnoldi method

I am trying to speedup the calculation of eigenvalues, given that I have good guesses for the eigenvectors. From what I know of Arnoldi/Lanczos, my good guesses should be helpful. Unfortunately, I am ...