Questions tagged [eigenvalues]

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4
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1answer
167 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
158 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 ...
3
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1answer
141 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
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2answers
313 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 ...
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0answers
439 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
129 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
74 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
729 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
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1answer
300 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
620 views

How can I plot eigenvalues?

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0
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1answer
268 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
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1answer
87 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
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1answer
174 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
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2answers
303 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
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1answer
277 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 ...
4
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0answers
169 views

What real symmetric matrices of this type can Mathematica find symbolic eigenvalues for?

I'm working on a problem calculating symbolic eigenvalues of matrices that always have a very simple form: they are real and symmetric and usually sparse. They have two distinct symbolic parameters. (...
4
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2answers
8k views

How to normalize a list of eigenvectors?

Here is a simple eigenvector problem solution m = {{2, Sqrt[15]}, {Sqrt[15], 4}}; v = Eigenvectors[m] However, the list of vectors v is not normalized. The ...
3
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1answer
199 views

Seemingly wrong eigenvectors for numerical matrix whose elements differ in scale by orders of magnitude

I stumbled upon an issue with computing eigenvalues of a matrix which I discovered while debugging some code which uses reconstructing the matrix from its eigenvalues/eigenvectors. First of all, here ...
3
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0answers
265 views

Irreducible Matrix [closed]

Biologist here, so my mathematic background isn't the best. So, I have a nonnegative 15x15 matrix and I'm getting eigenvalues higher than 1 - which are of interest to me. My problem, however, is that ...
4
votes
1answer
333 views

Plotting eigenvalues with different colours

Bug introduced in version 11 I would like to plot all the eigenvalues (functions of Bz) of a matrix in the same plot, so as for Mathematica to understand that they are different functions and to plot ...
5
votes
1answer
109 views

Coloring specific set of points in a plot

I have a large set of points.I get two bands of points in the graph which merge upon choosing suitable value of the parameters E1 and E2. My question is how to color these two sets of points ...
1
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2answers
141 views

Find the parameter values for my matrix for it to have imaginary eigenvalues

Say I have a matrix that depends on a parameter $u$. The following may be an example: a = {{1, u^3 + 2, 1}, {0, 1, u}, {1/u^2, 0, 1}}; My real problem is 12x12 ...
2
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0answers
125 views

Orthogonalization and normalization during eigendecomposition [duplicate]

I have the following simple code to compute the eigenspectrum of a complex symmetric matrix A, and its column of eigenvectors Q: ...
0
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1answer
181 views

Scree Plot Using Eigenvalues in Mathematica?

What is the best way to generate a Scree Plot (for Scree Test) using the Eigenvalues from the PCA? Here is what I am using right now: ...
7
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2answers
759 views

Calculating smallest eigenvalues by real part using Arnoldi method

Bug introduced in 8.0 or earlier and persisting through 11.3 According to the documentation, Eigenvalues[m,k] gives the first ...
3
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2answers
647 views

Visualizing Eigenvalues

I am not so adept at mathematica. Despite, indirectly, finding a few examples, I cannot find a particular plot I am looking for. The plot you see has a clear representation of complex eigenvalues. In ...
3
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1answer
185 views

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 (...
6
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1answer
470 views

NDEigensystem for structural vibration

Having installed version 11 I thought I would check an old Stack Exchange vibration problem using NDEigensytem. The old problem was Test a wooden board's vibration mode and I think this was before ...
4
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0answers
171 views

How to verify the convexity of a function?

I have an optimization problem with the following objective function in $(x,y)$ $$ A\log \left(\sum_{i=1}^n x_i\right)+\log\left(1-\frac{f}{n}\left(\sum_{i=1}^n\frac{x_i}{y_i}\right)\right) $$ where $...
5
votes
1answer
281 views

Eigenvalues of large symmetric matrices

When I try to compute the eigenvalues of the adjacency matrix of a very large graph I get, what can be charitably described as, garbage. In particular, since the graph is four-regular, the eigenvalues ...
3
votes
1answer
210 views

Increasing Plot3D speed when plotted function is Eigenvalue

This is probably a really simple fix, but I'm fairly new to Mathematica and am not sure how to do this properly. I know that trying to plot eigenvalues directly can be computationally expensive, so I'...
10
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1answer
5k views

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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