# Questions tagged [eigenvalues]

Questions on symbolically or numerically determining the eigenvalues of matrices (Eigenvalues, Eigensystem) or differential equations (DEigenvalues, DEigensystem, NDEigenvalues, NDEigensystem) in Mathematica. Also includes determining the eigenvalues of differential equations with DSolve or NDSolve.

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### Singular Value Decomposition of a matrix over the complex plane using parallel table

I have a big matrix $M(z)$ where $z$ is a complex number. The matrix is also dense. I am trying to compute the smallest singular value of the matrix over the complex plane. Since the computation at ...
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### Why is Mathematica not solving a differential eigenvalue problem with Robin boundary condition correctly?

I am trying to solve for the natural frequencies of a rod vibration problem. The BVP to be solved is u''[x]+\[Omega]^2 u[x] == 0 subject to the boundary conditions ...
94 views

### How to find the common eigenvectors of these commuting matrices?

Given matrices P and Q defined as P = {{x - I y, z}, {z, x + I y}}; Q = {{0, 1}, {1, 0}}; ...
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### Troubling using the arnoldi method

I have the following code: The first part is just defining the matrices, the error is at the end of the code. ...
655 views

### Is there a bug in Eigensystem[]?

Does Eigensystem[] produce incorrect output for symmetric matrices with integer components? The following eigensystem decomposition of a 12x12 matrix and its ...
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### Automatization of eigenvalue analysis

I am trying to make a code to extract the eigenvalues of an eigenfunction of an ODE, and then insert these eigenvalues in an operation. I start with the following, where sol is the eigenfunction of ...
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1 vote
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### Why is generating normalized random $1000 \times 1000$ matrices and plotting the eigenvalues so slow?

For each of the distributions $N(0,1)$ and $\pm 1$ equal probability and for each of $N \in \{5,10,20,50,100,200,1000\},$ I want to generate an $N \times N$ matrix with entries chosen from the ...
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### Efficient eigendecomposition of DPR1 matrices

I'm finding that the following bit is the bottleneck in my code ...
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### Why occur a giant increasing of absolute value of minimal eigenvalue with rise of the basis functions number?

I have the following code: code 1 ...
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### Schmidt Measure of a Graph State

Based on the definition of the Schmidt measure in this work https://www.arxiv-vanity.com/papers/quant-ph/0307130/, the following code was set up, but appears to generate errors. Is there a better way ...
• 3,128
141 views

### Generate real random matrix with some pure imaginary eigenvalues

I want to generate a random 4x4 matrix with real entries, one or some of whose eigenvalues is the pure imaginary number I or some other imaginary number. NOTICE The ...
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### Cells stuck at running after running after finding symbolic eigenvalues of a 4x4 matrix

I used the code below to calculate the eigenvalues of a 4x4 matrix symbolically. ...
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### How is the output (a list) of the "Eigenvalues" function ordered?

The documentation of the function Eigenvalues says that the Eigenvalues are sorted in order of decreasing absolute values. But what is if the absolute values are the same. For example when two ...
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### Incorrect eigenvalues obtained from NDEigensystem

I have a matrix H1 given by H1[kx_, ky_] := {{0, kx + ky}, {kx - ky, 0}}; and H2 which ...
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### Finding eigensystem using NDEigensystem

I am trying to calculate eigensystems for a matrix Ap, which I have provided an example of which in this thread. The matrix in general has a dependency on a ...
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### Problem in displaying output when finding eigenvalues of a Matrix

Basically I am trying to find symbolic eigenvalues of a 4x4 Matrix. Using the below code ...
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### Define a matrix with derivative variable and calculate its eigensystem

I have a 2x2 matrix that reads A = {{0.5, 3 (kx + ky) + x}, {2 (kx + ky) - x, -0.3 kx}}; Here kx and ...
• 749
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### How to write expression of the motion functions in Coulomb field so that it can be used as a basis in the matrix method for finding eigenvalues?

I would like to find the energy eigenvalues of the corresponding Hamiltonian (H = -1/2Laplacian -b/r * Exp[-a*r] , a, b - numbers) in the matrix way. For this, it is necessary to have a complete set ...
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1 vote
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### Finding the (symbolic) eigenvalues of a matrix with some assumption

I have the following 3$\times$3 symmetric matrix with symbolic entries. Meff = \begin{array}{ccc} 2 \beta \text{c12}^2 \text{c13}^2 \text{$\eta$11} \text{m1}+\alpha \text{c13}^2 \text{D31} \text{...
59 views

### Calculating Eigenvalues using xAct

I'm trying to calculate the eigenvalues of the following system which originates from here (Appendix B): \begin{align} i{\xi}_{0}\hat{\tilde{\gamma}}_{ij} &= 2i\tilde{\gamma}_{k(i}\xi_{j)}\...
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1 vote
69 views

### Why does the minimum eigenvalue sharply decrease when the number of basis functions increases from 37 to 38 and more?

I have the following Hamiltonian: H = -1/2 * Laplacian -1/r - 2 * r/5 * (Exp[-r * 1.6] + Exp[-r * 3.1]) I'm trying to find the minimum eigenvalue of this Hamiltonian using the matrix method. As basis ...
• 771
1 vote
145 views

### Eigenvalues of Coulomb potential

As it turned out in the previous question (Eigenvalues of A/r^2 + B*r^2 potential), in order to find the energies by the matrix method, it is necessary to have a complete set of basis functions. @...
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### Eigenvalues of A/r^2 + B*r^2 potential

I would like to find the energies of a system in a matrix way. The system has the following Hamiltonian: H1 = -1/2Laplacian +(A1/r^2)+(B1r^2) I use radial functions as basis functions: Psi1[r_, n_] =...
• 771
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### Why do different calculations give different eigenvalues?

I find the eigenvalues of the Hamiltonian in two ways - numerically and matrix . Why do different calculations give different eigenvalues? The Hamiltonian is H = -1/2*Laplacian -(2/r) It can be seen ...
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1 vote
59 views

### 3D plot is noisy

I have the following 3x3 matrix, dependent on the variables $k_{x}$,$k_{y}$ : ...
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### Confusion in Eigenvalue and eigenfunction distribution using NDEigensystem [duplicate]

I have been using NDEigensystem to solve the Schrodinger equation for different potentials. However, whenever the potential has its minimum in the negative y-axis, ...
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### Graph the eigenvalue as a function of x and y

I want to write down a small program that would have as input an eigenvalue, I take it directly from the lists of eigenvalues. In fact, the eigenvalue is a function of x and y. What I would like to do ...
1 vote
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