Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [eigenvalues]

The tag has no usage guidance.

2
votes
1answer
85 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
32 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
153 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
122 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
103 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) \, \...
8
votes
1answer
206 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
86 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
votes
0answers
45 views

JordanDecomposition: Error Mesage eivn

I want to calculate the JordanDecomposition of the follwoing matrix: That is ...
4
votes
1answer
147 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
141 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
50 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
65 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
52 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 ...
30
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
50 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
142 views

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

In Mathematica, I computed the following: ...
2
votes
1answer
59 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
336 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
votes
1answer
25 views

Eliminate the higher powers of eigenvalues of a matrix

I want to found de eigenvalue of following matrix ...
2
votes
1answer
50 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
59 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
79 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
55 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
107 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
132 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
283 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
61 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
71 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
43 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
48 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
108 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 ...
5
votes
1answer
88 views

Finding the orthogonal diagonalizing similarity of a symmetric matrix

I'm aware that there are some questions similar to this here, but none that could solve my problem. So, I have to diagonalize a symmetric symbolic matrix $m$ (to be seen below) and obtain the ...
1
vote
1answer
69 views

Eigenvector of a non-negative matrix [closed]

A very basic question. The Perron–Frobenius theorem states: The largest eigenvalue of a matrix with non-negative entries has a corresponding eigenvector with non-negative values. I have a matrix ...
7
votes
2answers
164 views

Analytic solution to Orr-Sommerfeld-Squire equations for a special case

Hello everybody in Mathematica SE. Although my question is related to flow stability analysis, this should be a general application of MMA to solve a system of ODEs. Thank you for your suggestion! ...
2
votes
1answer
54 views

Taking a derivative of an eigenvector

I'm trying to calculate the derivative of an eigenvector that I obtain by ...
5
votes
1answer
132 views

How to plot complex eigenvalues of a matrix?

I have a matrix , for instance, like this : matrix[a_ ] := {{0, a}, {-a, 1}}; Eigenvalues[matrix[a]] and this give the eigenvalues that depends on ...
0
votes
0answers
22 views

Discrepancy in solutions given by Solve function

I wish to solve for the parameters g1 and/or g2 with which the eigenvalues of the following Matrix ...
6
votes
1answer
110 views

Inconsistency in eigenvalues of matrices in a specific form (sparse & non-Hermitian)

Suppose one has a non-Hermitian sparse matrix defined as below ...
0
votes
0answers
55 views

Mathematica can solve the eigenvalues of a large sparse non-Hermitian (non-symmetrical) matrix?

The Arnoldi algorithms of function "Eigensystems" in Mathematica can be used to solve the eigenvalues of a Large Sparse non-Hermitian (non-symmetrical) Complex matrix?
6
votes
2answers
138 views

Solving eigenvalue BVP with an interface

I have a boundary-value problem, that is defined over two adjacent regions with an interface in the middle, that contains an eigenvalue $\lambda$. The boundary conditions and the equations are ...
5
votes
2answers
120 views

Unable to evaluate Eigenvalues and Eigenvectors for a matrix

I have the following 3X3 matrix M and I wish to find its eigenvectors and eigenvalues ...
3
votes
2answers
212 views

How to numerically solve the Schrödinger equation for Lennard-Jones potential?

Hi I have a potential like below: V[x_]:= 102*(4343/x^12 - 650/x^6) + 33/x^2 Which is a kind of modified Lennard-Jones potential. Schrödinger equation is 1D ...
0
votes
1answer
44 views

How can I find eigen values and eigen vectors of a symbolic matrix? [closed]

How can I find eigenvalues and eigenvectors of this system given as a matrix? ...
1
vote
0answers
39 views

Solve the 'Eigenvalue' problem efficiently [closed]

Usually, an eigenvalue of a matrix A is defined as |A-b*I|=0, where I is the identity matrix and |..| is for the determinant. Now my question becomes a little different, let's say A is a function of ...
2
votes
1answer
121 views

Plotting eigenvalues in one plot for three different parameters

I am trying to plot eigenvalues of the matrix with different $W$. I can plot them separately but I want to merge them in a single plot with different colors. Is there any other type of plot other than ...
1
vote
1answer
30 views

Obtain needed Kronecker products from output of Eigensystem[]

Eigensystem[M] gives a list of the eigenvalues and eigenvectors of the square matrix M, i.e. {{val1,val2,...},{vec1,vec2,...}}. I need a routine that will ...
0
votes
1answer
94 views

Eigenvector for specific eigenvalue [closed]

I can't find guidance in the documentation center for how to retrieve the eigenvector(s) of a matrix associated to a specific eigenvalue. My first question is what the command is to do that. I would ...