# Questions tagged [eigenvalues]

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### 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 ...
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### 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: ...
111 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? \...
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### 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 ...
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### 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 ...
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### 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., ...
108 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 ...
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### 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 ...
147 views

### Eigen value solution of coupled ODEs

I want an eigen value solution of following coupled ODEs: But the code showing errors. ...
69 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, ...
67 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. ...
380 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 ...
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### 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 ...
898 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. ...
53 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,...
104 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. ...
38 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 ...
135 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 ...
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### How can one do looping with matrices for large N (= 100, 200, etc), where N is the matrix size of a given form, to get N eigenvalues?

I want to generalize the following to large N: ...
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### 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 ...
110 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 ...
76 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 ...
104 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 ...
116 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: ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### JordanDecomposition: Error Mesage eivn

I want to calculate the JordanDecomposition of the follwoing matrix: That is ...
379 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 ...
174 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 ...
76 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 \...
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### 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 ...