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Questions tagged [eigenvalues]

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4
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0answers
48 views

Orthogonal matrix decomposition of symmetric matrix?

If matrix mat is symmetric, we should be able to decompose it into eigenvalue matrix matJ and orthogonal matrix ...
2
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2answers
69 views

Unable to evaluate Eigenvalues and Eigenvectors for a matrix (2)

I have posted a similar question last year pertaining to this issue. Here's a link to my post together with the solution given: Unable to evaluate Eigenvalues and Eigenvectors for a matrix I have ...
2
votes
1answer
59 views

How can I tell if a matrix is ill-conditioned or Singular by using the Eigensystem function(or LUDecomposition)?

I'm using the Eigensystem function, and I'm trying figure out whether or not it is singular or ill-conditioned. I'm using the function as so: ...
0
votes
0answers
50 views

Different Outputs When Calculating Within a Table and Seperately [closed]

I have a matrix which looks like this: $$\begin{pmatrix} a & e & 0 & 0 \\ 1 & b & 1 & 0 \\ 0 & 1 & c & 1 \\ 0 & 0 & 1 & d \\ \end{pmatrix}$$ where $\{ ...
1
vote
2answers
51 views

Table Command with multiple Variables

I am new to Mathematica, so I'm not sure about the ins and outs of what's possible and what is not. I am trying to view the eigenvalues of multiple matrices at once. In particular, this matrix: $$\...
0
votes
1answer
35 views

Creating functions from a eigenvalues output [on hold]

I need to create a function with the Eigenvalues output. The problem in question is that I need to manipulate variables from the eigenvalues and then plotting them. ...
2
votes
3answers
53 views

Plotting Solve output automatically

I am trying to solve a characteristic polynomial and plotting its output. The problem is that I do not know how to take the output automatically. My current code is ...
2
votes
1answer
32 views

Eigenvalue decomposition of a density matrix not reproducing original density matrix

A density matrix $\rho$ in quantum mechanics is defined as any self adjoint and positive semidefinite matrix with a trace or 1. It can be expanded into sets of pure states such that $\rho=\sum_{i}p_{...
0
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1answer
47 views

Strange answer for Eigenvalues of a 4x4 matrix [duplicate]

I am getting these strange eigenvalues of this simple looking 4-dimensional matrix: ...
2
votes
1answer
31 views

Performance Tuning: Construction of Matrix with Summations

I am trying to solve an eigenvalue problem of a large matrix. The issue is that it takes too much time to construct this large matrix. This is the code that I built: ...
1
vote
2answers
60 views

Eigenvalues error: “The method ”Banded“ accepts only sparse matrices with elements that are machine-real or machine-complex numbers”

I'm having one issue with the Eigenvalues function in some code priorly discussed here. There the example is tridiagonal, but here, let us consider this simple ...
1
vote
0answers
42 views

Fast Plot3D, failing NIntegrate, and reckless surgery

I have a square matrix, m which depends on kx and ky. It isn't Hermitian, but it does have ...
2
votes
1answer
99 views

What am I doing wrong when trying to plot this function?

I'm trying to reproduce the computations of this paper and I'm running into some troubles because I'm rather new to Mathematica. In the paper's page 4, in figure 2 the authors show a plot of a ...
5
votes
0answers
42 views

Where is the mistake in computing the particular eigenvector of the following DFT Matrix?

I have the following matrix (the DFT Matrix for N = 3) $$W = \frac{1}{\sqrt{3}}\begin{pmatrix} 1 & 1 & 1 \\ 1 & e^{-\frac{i 2 \pi}{3} } & e^{\frac{i 2 \pi}{3} } \\ 1 & e^{\frac{...
4
votes
1answer
96 views

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 ...
3
votes
1answer
273 views

1st-order linear ODE system gives inaccurate/biased solutions

Consider an ODE eigensystem $$ t(y+\frac{1}{s})a(y)+[(q+\frac{1}{2}+\frac{s}{2}y)+s(y\partial_y+\frac{1}{2})]b(y)=\lambda a(y)\\ t(y+\frac{1}{s})b(y)+[(q+\frac{1}{2}+\frac{s}{2}y)-s(y\partial_y+\frac{...
2
votes
1answer
105 views

How to solve this 2nd-order ODE with quadratic coefficients?

Consider an ODE eigensystem $$ \begin{bmatrix} 0 & d_1-\mathrm id_2 \\ d_1+\mathrm id_2 & 0 \end{bmatrix} \begin{bmatrix} a(y) \\ b(y) \end{bmatrix} = \lambda \begin{bmatrix} a(y) \\ b(...
0
votes
0answers
41 views

Plot Eigenvalue Data

`kmin = 0; (* min wave number *) kmax = 5; (* max wave number *) nopoints = 51; step = (kmax - kmin)/(nopoints - 1); ktable = Table[k, {k, kmin, kmax, step}];` I ...
3
votes
2answers
174 views

Eigen values of a third order linear homogenous ODE

From a system of PDEs where i used the following ansatz: $$\theta_w(x,y) = e^{-\beta_h x} f(x) e^{-\beta_c y} g(y)$$. $F(x) := \int f(x) \, \mathrm{d}x$ and $G(y) := \int g(y) \, \mathrm{d}y$ So, $$\...
3
votes
3answers
131 views

Plotting eigenvalue function along a path with correct coloring

This question has multiple parts to it. The setup is that I have a matrix that is a function of two parameters a and b. I wish to plot the eigenvalues of this matrix along a general path in the a-b ...
1
vote
1answer
112 views

How Can We Solve The Eigenvalues of partial-integral equation?

Here, my problem is that $$ \left(\int_{-L_0}^{L_0} \left(\int_{-L_0}^{L_0}\mathrm e^{-(x-x_1)^2-(y-y_1)^2} ({\bf u_{\lambda}}(x_1, y_1) + {\bf v_{\lambda}}(x_1, y_1)) \, \mathrm dx_1\right) \, \...
9
votes
1answer
259 views

How to solve this 2nd-order ODE with singularity?

I tried solving the eigenvalue problem of a 2nd-order ODE $$[b^2(k-2)^2y^2-2b(k-2)(1+2ky)+4k^2+b^2(k-2)3y]f(y) \\- 3b(3by-2)f'(y)\\-(3by-2)^2f''(y)=\lambda f(y)$$ with ...
0
votes
1answer
95 views

How to compute Eigenvalues of a large symbolic matrix?

I am trying to find eigenvalues for a big matrix having symbolic elements. Basically I am trying to find values of lambda for which matrix $(A-\lambda)$ is singular. For small matrices, we generally ...
0
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0answers
50 views

JordanDecomposition: Error Mesage eivn

I want to calculate the JordanDecomposition of the follwoing matrix: That is ...
4
votes
1answer
190 views

Solving the eigenvalue problem for a double well potential using a 1D particle in a box as a basis set

My first question is how would I go about getting the 1D particle in a box eigenfunctions using matrix techniques and how would I use the particle in a box eigenfunctions as a basis set for the ...
3
votes
1answer
152 views

Eigenvalues of a non-Hermitian complex periodic potential

I have an eigenvalue problem: $$-\frac{d^2}{dx^2} \psi(x) +V(x)\psi(x) = E \psi(x)$$ where $V(x)$ is a complex periodic potential: $$V(x) = 4[\cos^2(x) + i 0.3 \sin(2x)]$$ It has been claimed that ...
3
votes
1answer
52 views

Spectrum of eigen values for coupled differential equations

How do I obtain a spectrum of eigenvalues for my system of coupled differential equations? $$ kf''(\theta) + \epsilon_{1} f(\theta) + a\cos(b \theta + c) g(\theta) = \lambda f(\theta),\\ a\cos(b \...
0
votes
0answers
84 views

How to obtain left and right eigenvectors of a general complex matrix with degenerate eigenvalues?

I'm looking to obtain the left and right eigenvectors of a general complex matrix. The left eigenvectors satisfy the equation: $\phi^L_i L = \lambda_i \phi^L_i$, with $\lambda_i$ being the $i$th ...
2
votes
1answer
53 views

ParallelDo gives different solution to Eigensystem

I am trying to calculate the eigensystem of a large matrix (e.g. 256x256). I have found that when I do this within a ParallelDo (because I am actually calculating many of these eigensystems), the ...
31
votes
1answer
1k views

Wrong eigenvalues from a sparse matrix: eigenvalues are nonreal

Bug introduced in 9.0 or earlier and persisting through 11.3. I notice in the following example that wrong complex eigenvalues are resulted if calculating from a Hermitian sparse matrix, which should ...
3
votes
1answer
51 views

Solving $\det{(A+\epsilon B)}=0$ for large, symmetric and dense $A$ and $B$

In an algorithm I am writing, I need to solve the equation $$ \det{(A+\epsilon B)} = 0, $$ for the smallest value of $\epsilon$, given large ($n$x$n$ ideally up to 150x150), dense and symmetric A ...
0
votes
1answer
223 views

Eigenvalues for a $ 4 \times 4 $ matrix [duplicate]

In Mathematica, I computed the following: ...
2
votes
1answer
65 views

Inaccurate zero eigenvalues for 7*7 matrix [closed]

I have symbolic entries for all the elements of a 7*7 matrix. At the symbolic level Eigenvalues gives two zeroes and five others that are extremely complicated. At ...
11
votes
2answers
342 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 ...
0
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1answer
25 views

Eliminate the higher powers of eigenvalues of a matrix

I want to found de eigenvalue of following matrix ...
2
votes
1answer
58 views

Eigensystem for simple equi-correlation matrix

I'm trying to get a set of eigenvectors for a correlation matrix, but getting stuck, maybe because I do not properly normalize them. For example, the following code works, in the sense that I get back ...
0
votes
1answer
63 views

How to solve a matrix $ Ax=0 $, where matrix $ A $ is a function of $ ω^2 $ [closed]

I have a matrix $ A $ which depends on $ ω^2 $. I wanted to solve for $ ω $. The usual procedure is taking the Det[A] and equate to zero and solve for it. How can I ...
0
votes
1answer
116 views

Det, MatrixRank and Eigenvalues

I consider myself to be an inexperienced Mathematica user so maybe someone could point out what am I doing wrong. In short, here is what I want to get: suppose that there is a matrix of dimension $ N ...
1
vote
1answer
93 views

NDEigensystem to find eigenvalues and eigenfunctions of coupled differential equations:

I would like to numerically solve the following system of coupled differential equations: ...
0
votes
0answers
57 views

NDEigensystem boundary conditions

I am attempting to solve the Schrodinger 1-D time independent equation for the eigenfunctions and eigen-energies of the piecewise potential described in the attached image of my code. I need to ...
1
vote
1answer
136 views

Having trouble working with two mass, three spring dynamic system

I am following a dynamic analysis example https://www.math24.net/mass-spring-system/ and trying to implement it in Mathematica. However, I am having trouble even getting simple properties like the ...
3
votes
2answers
139 views

Schrödinger equation for a hydrogen atom and lack of memory

I'm trying to solve the Schrödinger equation for a hydrogen atom in the Cartesian coordinate system. This is my code ...
9
votes
5answers
303 views

NDEigenvalues vs. FindRoot for finding the eigenvalues of Airy equation?

Say I am trying to find the first 5 eigenvalues of the differential equation $f''(x)=\lambda x f(x)$, on the interval [-1,0], with boundary conditions $f(-1)=f(0)=0$. I will try to do this 3 ways, ...
2
votes
2answers
53 views

How to return multiplicity of each eigenvalue?

I could not find the information so maybe someone know if it possible. I have a matrix which has several degenerated eigenvalues and I would like Mathematica to return the multiplicity of each ...
3
votes
0answers
67 views

Antisymmetric Matrix Eigenvector Normalization

So, I have a complex $4n \times 4n$ antisymmetric matrix, $A$ and it has a non-degenerate spectrum. The matrix $A$ then has eigenvalues given by $$ \beta_{1}, -\beta_{1}, \beta_{2}, -\beta_{2}, ... , ...
1
vote
1answer
108 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 \...
0
votes
0answers
51 views

Density map for complex and imaginary parts of eigenvalues on one graph

I have three eigenvalues of a particular 3x3 matrix. Namely: ...
2
votes
1answer
52 views

Recover non-normalized solutions from NDEigensystem

Are there certain commands, or some mathematical trick I can use to recover the non-normalized solutions from NDEigensystem? My equation of interest is of the form $u''(x)+f(x)u(x)=\lambda u(x)$ I ...
6
votes
1answer
123 views

Eigensystem returns vectors which are not eigenvectors

Short synopsis: for a specific family of sparse matrices, the eigensolver seems to be unstable (kernel quitting) for certain examples, and when it works it seems to consistently return vectors which ...