# Questions tagged [eigenvalues]

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### Mathematica won't give eigenvectors but Wolfram Alpha will? What am I doing wrong?

If I ask Mathematica to find the eigenvectors and eigenvalues of the matrix: ...
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723 views

### Solving this challenging ODE

Consider the ODE: $$w^{(4)}(x) + (L-x)w''(x) - w'(x) = 0$$ with some of the following boundary conditions: free: $w'' = 0$, $w'''=0$, clamped: $w = 0$, $w'=0$, pivot: $w = 0$, $w''=0$. Two such ...
383 views

### Making an interactive visualization of the eigenvectors of two-dimensional matrices

I've recently stumbled upon this very nice interactive visualization of eigenvectors of two-dimensional matrices, and how powers $A^k$ act on various vectors. How can this sort of visualization be ...
596 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 ...
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### 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 ...
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### NDEigenvalues complains not Hermitian with large dimension differential operator

The following snippet calculates eigenvalues and eigenfunctions of a null operator (just as an example): ...
248 views

### Finding the eigenvalues (diagonalizing) of a block-diagonal matrix

I have a large $2^N \times 2^N$ matrix. It is the exact Hamiltonian of a spin chain model which I have generated with code I wrote in Fortran. The code block diagonalizes the Hamiltonian into constant ...
453 views

### Wrong eigenvalues from a sparse matrix

Bug introduced after 5.0, in or before 8.0 and persisting through 12.0. I notice in the following example that wrong smallest 2 eigenvalues are resulted if calculating from a sparse matrix. But it ...
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### Solving eigenvalue BVP with an interface

I have a boundary-value problem, that is defined over two adjacent regions with an interface in the middle, that contains an eigenvalue $\lambda$. The boundary conditions and the equations are ...
7k views

### How to normalize a list of eigenvectors?

Here is a simple eigenvector problem solution m = {{2, Sqrt}, {Sqrt, 4}}; v = Eigenvectors[m] However, the list of vectors v is not normalized. The ...
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### 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 ...
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### How can one do looping with matrices for large N (= 100, 200, etc), where N is the matrix size of a given form, to get N eigenvalues?

I want to generalize the following to large N: ...
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### Unable to evaluate Eigenvalues and Eigenvectors for a matrix

I have the following 3X3 matrix M and I wish to find its eigenvectors and eigenvalues ...
53 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,...
314 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, ...
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### Discontinuities in eigenvalues plotting with Plot3D

I have a 6x6 matrix, depending on 2 variables kx and ky and defined as the sum of the two following matrices (...
293 views

### How to collect eigenvectors corresponding to only positive eigenvalues?

Let us consider a matrix of order $n \times n$ with $n/2$ positive and $n/2$ negative eigenvalues. How to collect $n/2$ eigenvectors corresponding to positive eigenvalues in a matrix of order \$n \...