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Questions tagged [eigenvalues]

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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 ...
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), ...
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 ...
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 ...
166 views

Can NDEigensystem use arbitrary precision arithmetic?

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

Eigenvalues broken in 11.2?

Bug introduced in 11.1.0 and fixed in 11.3.0 The code ...
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 ...
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). ...
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{...
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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
123 views

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? ...
544 views

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...
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 ...
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 ...
568 views

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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. ...
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: ...
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'...
265 views

Plotting complex eigenvalues of a matrix as a function of a parameter: developing a color function to represent imaginary part

Consider the example below: ...
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 ...