# Questions tagged [eigenvalues]

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### Finding the Eigenvalues for big matrices

To start I have the following matrix (not so big) I want to find the Eigenvalues in terms of kx and ky. I tried to use the classical ...
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### Plotting eigenvalues

I am trying to reproduce figure 10 in the linked paper. The authors have used Matlab bvp4c function to find multiple solutions for the system of ODE and then carried out the stability. Here is my ...
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### Proving the positive semidefiniteness of a 6X6 symbolic matrix

Specifically, I want to check the positive semidefiniteness of the following 6X6 symbolic matrix ...
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### Problem with QRDecomposition [closed]

I was using Mathematica for the QR decomposition method. But I got strange results. I wanted to find eigenvalues of a matrix, say ...
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### Different result from utilizing of eigenvalues and eigenvectors commands

I have a matrix as a function of a parameter like ...
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### Using Eigensystem to solve eigenvalue problem [duplicate]

I'm trying to solve an eigenvalue problem of the form: $\textbf{A}\vec{x}=\lambda \textbf{B}\vec{x}$, where A and B are square matrices, $\lambda$ are the eigenvalues and $\vec{x}$ the eigenfunctions. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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.....
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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 ...
582 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 ...