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Questions tagged [eigenvalues]

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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. (...
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 ...
182 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 ...
248 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 ...
306 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 ...
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 ...
135 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 ...
118 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: ...
170 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: ...
678 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 ...
617 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 ...
177 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 (...
450 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 ...
143 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 \$...
256 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 ...