Questions tagged [eigenvalues]

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4
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1answer
53 views

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 ...
3
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2answers
898 views

Two matrices that are not similar have (almost) same eigenvalues [closed]

I have two matrices $$ A=\begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix} \quad \text{ and } \quad B=\begin{pmatrix} d & e & f \\ d & e &...
0
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1answer
87 views

How can I get the Eigen system of a certain matrix? [closed]

How can I get Eigen system of c, where c = a - iota * b? Please help me to find the Eigen system in a nice form. ...
3
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0answers
58 views

Derivative of eigenvalues

I work with 4x4 Hermitian matrices (r). I want to calculate a derivative of a function f[t,r] (ff[t_,r_]=1/2*D[f[t,r],t]), where the function f depends on the absolute value of the eigenvalues of r. ...
3
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2answers
748 views

Problem with Eigenvectors

When I want to calculate eigenvectors of the following matrix in Mathematica the only answer it gives me is zero vector, anybody knows how to fix this? here's my matrix : \begin{equation} X=\left(\...
5
votes
2answers
109 views

How to show just one function from a stored plot?

Q: Is there a general way to remove particular functions from a previously stored call to a plot function? Here is a specific example: ...
8
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0answers
181 views

DEigenvalues and NDEigenvalues return different values

In the following example, DEigenvalues and NDEigenvalues return different results despite having identical arguments. Does anyone know why? (I use Mathematica 11.3) ...
7
votes
1answer
121 views

How to solve this 1st-order linear ODE system with a few discrete eigenvalues?

I am trying to solve the eigensystem of a 1st-order linear ODE system in the region $(-\infty,\infty)$ and with Dirichlet boundary condition at the infinities $$ -i\partial_xu(x)+f^*(x)v(x)=\lambda u(...
0
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0answers
40 views

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 ...
0
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0answers
119 views

Finding eigenvalues of a differential operator

I am trying to get the eigenvalues of the following differential operator $$L\psi(r) = -f \partial_r (f \partial_r \psi(r)) + V \psi(r)$$ which must satisfy (obviously) $$L \psi(r) = \omega^2 \psi(...
0
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0answers
37 views

Some issues with DEingesystem

I would like to solve (get its eigenvalues/vectors) the Sturm-Liouville problem, for the following differential operator: $L =\partial_{r} \partial_{r} \psi(r)$. Also, I would like to impose the ...
0
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0answers
49 views

Eigenvectors of Hermitian matrices [duplicate]

I asked a similar question in the physics stack exchange, but realized my question is probably more suited here. For any Hermitian matrix $H = H^{\dagger}$ we can write $H = P DP^{\dagger}$ where $P$ ...
0
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0answers
31 views

Ordering of Eigenvectors [duplicate]

I am interested in computing the derivatives of the eigenvalues of a certain $n\times n$ Hermitian matrix $M(t)$. I know I can do this easily since I know the exact expression for $\dot{M}$, and the ...
4
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2answers
205 views

Help with coding a matrix

I have a $n \times n$ matrix $A$ with a full set of eigenvalues $\lambda$ including repetitions. I want to create the following $i \times i$ matrix: $$\left(\sum_{a=2}^i (a-1) |a-1⟩⟨a| \right) + \...
1
vote
1answer
138 views

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 ...
0
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2answers
70 views

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 ...
0
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0answers
16 views

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 ...
5
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2answers
120 views

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 ...
6
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3answers
515 views

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 ...
0
votes
1answer
52 views

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 ...
5
votes
1answer
65 views

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 ...
5
votes
1answer
574 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 ...
3
votes
1answer
72 views

How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?

Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows. ...
34
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2answers
787 views

Eigenvalues broken in Version 12.0

Bug introduced in 12.0. The following code calculates the eigenvalues of a certain complex matrix, which come in pairs of opposite complex numbers. Therefore one can check whether the sum of all ...
0
votes
1answer
90 views

Using multiple boundary conditions with NDEigensystem

I'm quite new to Mathematica and to Stack Exchange so I apologise if this question has already been answered. I've recently been trying to solve a partial differential equation to find the ...
5
votes
1answer
135 views

Speed up selecting positive eigenvalues repeatedly

I have a smallish (e.g. 2x2 or 4x4, but ideally up to 10x10) non-symmetric square matrix $\mathbf{A}(x)$. I need to define a function $f(x)$ which is the sum of the eigenvalues with positive real part ...
2
votes
1answer
92 views

Using NDEigensystem to find 100 eigenvalues

I'm using "NDEigensystem" to calculate a Sturm-Liouville problem, for which the first 100 eigenvalues are needed. The code is like this: ...
1
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1answer
66 views

Why am I getting incorrect Eigenvectors for my matrix? [closed]

When i try and compute the Eigensystem using Mathematica i am getting negative values for my Eigenvector, but my Eigenvalues are correct but my Eigenvectors are incorrect and i do know why is that? \...
1
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0answers
83 views

Problems with the eigenvalues calculated using NDEigenvalue

I'm trying to solve a Sturm-Liouville problem like $\qquad -\psi''(z)+(\frac{1}{z}+2\,z)\psi'(z)=\lambda\,\psi(z)$ using NDEigensystem in order to learn how to ...
3
votes
2answers
76 views

Solution to eigenvalue BVP using NDEigensystem to high precision

I'm trying to solve linear (non-self-adjoint) boundary-value problems to as high precision as possible (optimally 1e-15). For example, the below code solves for the first 5 eigenvalues of the harmonic ...
0
votes
1answer
40 views

Simplifying an expression involving a matrix and functions of it

I have implemented the following two matrices in Mathematica in order to compute s, but I don't know how I can further simplify the resulting expressions, e.g., ...
2
votes
1answer
92 views

Eigenvalue dependent boundary conditions- mathematica

I am dealing with an eigenvalue problem whose boundary conditions are also eigenvalue dependent. Could anyone please comment whether Mathematica can numerically solve such a problem? For boundary ...
0
votes
1answer
84 views

Obtaining eigenvectors without using Eigenvectors

Introduction I am trying to obtain the eigenvectors of a unitary matrix $M(k)$ which depends on a parameter k. This matrix $M(k)$ has dimension 6, and while for general matrices of dimension 6 it's ...
1
vote
2answers
145 views

Eigen value solution of coupled ODEs

I want an eigen value solution of following coupled ODEs: But the code showing errors. ...
2
votes
1answer
66 views

Efficient computation of matrices involving large sums of KroneckerDelta's

I was wondering if one could benefit from Mathematica's rich linear algebra methods for diagonalizing 2nd rank tensors. Namely, in the context of systems (fluids) comprised of capsule-like particles, ...
3
votes
1answer
64 views

Evaluating Hough functions by using NDEigensystem on the Laplace tidal equation

Currently I am looking into the use of Mathematica to solve the classical tidal equation of M. Laplace: $$\mathcal{F}\Theta+\gamma\Theta=0$$ whose eigenfunctions $\Theta$ are the Hough functions. ...
6
votes
2answers
346 views

Using NDEigensystem to solve the Mathieu equation

To be able to apply the differential equation capabilities of Mathematica to my graduate thesis, I am trying to apply NDEigensystem to an eigenproblem whose solution I know, but I am having some ...
0
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0answers
45 views

Why is this iterative process with matrix calculation so slow?

I am trying something similar to the following code with Ntime as large as 100 or so. Now it's very slow as shown by the Ntime=3 ...
5
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2answers
894 views

Noise in Eigenvalues plot

I am trying to Plot Eigenvalues of a Hamiltonian, but I am getting noisy plot, which is incorrect. Here is the code. ...
3
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0answers
51 views

Interface points of NDEigensystem

When solving an eigenvalue problem with "NDEigensystem", e.g. a 1D Eigenvalue problem with the interval composed of different materials, which should be solved by the pure numerical method such as FEM,...
2
votes
1answer
85 views

Meshing control of NDEigensystem

I have to solve an Eigenvalue problem originating from the Electrodynamics. It is a 2-D problem with a rectangular region. More specifically, there is a hole on a rectangle made by magnetic material. ...
1
vote
1answer
35 views

Defining a function that outputs a matrix, and later finding its eigenvalues

I am trying to do the following: I have a simple 2x2 matrix that depends on three parameters (physically -- momentum coordinates kx, ky, kz). Then I want to replace each of these parameters by a ...
4
votes
2answers
128 views

Efficiently find all values of parameter such that any of the eigenvalues of a matrix is equal to 1

I wish to find all values for a parameter such that my matrix has an eigenvalue of 1. Here is an example 16-by-16 matrix with elements depending on the parameter x ...
2
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2answers
102 views
1
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1answer
88 views

How to write the equation into matrix form [closed]

$[(a+k_i)^2+(b+k_j)^2]X_{i,j}-\sum_{m,n}V_{m,n}X_{i-m,j-n}=\mu X_{i,j}$. where $-N\le i,j\le N$ Here we can set $ N=10,a =1, b=1$ and $V_{m,n}$ is the matrix element of $V$. Once I write the ...
4
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0answers
78 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 ...
0
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0answers
71 views

Diverging solution to radial equation

I want to solve a seemingly simple eigenvalue problem. I have a fixed set of boundary conditions given and want to change the complex parameter omega in to minimize exponentially falling solutions for ...
2
votes
2answers
96 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
70 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: ...
1
vote
2answers
60 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: $$\...