Questions tagged [eigenvalues]
Questions on symbolically or numerically determining the eigenvalues of matrices (Eigenvalues, Eigensystem) or differential equations (DEigenvalues, DEigensystem, NDEigenvalues, NDEigensystem) in Mathematica. Also includes determining the eigenvalues of differential equations with DSolve or NDSolve.
437
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Singular Value Decomposition of a matrix over the complex plane using parallel table
I have a big matrix $M(z)$ where $z$ is a complex number. The matrix is also dense. I am trying to compute the smallest singular value of the matrix over the complex plane. Since the computation at ...
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Why is Mathematica not solving a differential eigenvalue problem with Robin boundary condition correctly?
I am trying to solve for the natural frequencies of a rod vibration problem. The BVP to be solved is
u''[x]+\[Omega]^2 u[x] == 0
subject to the boundary conditions
...
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4
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1
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How to find the common eigenvectors of these commuting matrices?
Given matrices P and Q defined as
P = {{x - I y, z}, {z, x + I y}}; Q = {{0, 1}, {1, 0}};
...
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3
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1
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Troubling using the arnoldi method
I have the following code:
The first part is just defining the matrices, the error is at the end of the code.
...
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7
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1
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655
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Is there a bug in Eigensystem[]?
Does Eigensystem[] produce incorrect output for symmetric matrices with integer components?
The following eigensystem decomposition of a 12x12 matrix and its ...
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47
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Automatization of eigenvalue analysis
I am trying to make a code to extract the eigenvalues of an eigenfunction of an ODE, and then insert these eigenvalues in an operation.
I start with the following, where sol is the eigenfunction of ...
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1
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77
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Why is generating normalized random $1000 \times 1000$ matrices and plotting the eigenvalues so slow?
For each of the distributions $N(0,1)$ and $\pm 1$ equal probability and for each of $N \in \{5,10,20,50,100,200,1000\},$ I want to generate an $N \times N$ matrix with entries chosen from the ...
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3
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275
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Efficient eigendecomposition of DPR1 matrices
I'm finding that the following bit is the bottleneck in my code
...
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Why occur a giant increasing of absolute value of minimal eigenvalue with rise of the basis functions number?
I have the following code:
code 1
...
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1
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118
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Schmidt Measure of a Graph State
Based on the definition of the Schmidt measure in this work https://www.arxiv-vanity.com/papers/quant-ph/0307130/, the following code was set up, but appears to
generate errors. Is there a better way ...
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2
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Generate real random matrix with some pure imaginary eigenvalues
I want to generate a random 4x4 matrix with real entries, one or some of whose eigenvalues is the pure imaginary number I or some other imaginary number.
NOTICE
The ...
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Cells stuck at running after running after finding symbolic eigenvalues of a 4x4 matrix
I used the code below to calculate the eigenvalues of a 4x4 matrix symbolically.
...
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2
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How is the output (a list) of the "Eigenvalues" function ordered?
The documentation of the function Eigenvalues says that the Eigenvalues are sorted in order of decreasing absolute values. But what is if the absolute values are the same. For example when two ...
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51
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Incorrect eigenvalues obtained from NDEigensystem
I have a matrix H1 given by
H1[kx_, ky_] := {{0, kx + ky}, {kx - ky, 0}};
and H2 which ...
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Finding eigensystem using NDEigensystem
I am trying to calculate eigensystems for a matrix Ap, which I have provided an example of which in this thread. The matrix in general has a dependency on a ...
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Problem in displaying output when finding eigenvalues of a Matrix
Basically I am trying to find symbolic eigenvalues of a 4x4 Matrix. Using the below code
...
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Define a matrix with derivative variable and calculate its eigensystem
I have a 2x2 matrix that reads
A = {{0.5, 3 (kx + ky) + x}, {2 (kx + ky) - x, -0.3 kx}};
Here kx and ...
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How to write expression of the motion functions in Coulomb field so that it can be used as a basis in the matrix method for finding eigenvalues?
I would like to find the energy eigenvalues of the corresponding Hamiltonian (H = -1/2Laplacian -b/r * Exp[-a*r] , a, b - numbers) in the matrix way. For this, it is necessary to have a complete set ...
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Finding the (symbolic) eigenvalues of a matrix with some assumption
I have the following 3$\times$3 symmetric matrix with symbolic entries.
Meff =
\begin{array}{ccc}
2 \beta \text{c12}^2 \text{c13}^2 \text{$\eta $11} \text{m1}+\alpha \text{c13}^2 \text{D31} \text{...
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Calculating Eigenvalues using xAct
I'm trying to calculate the eigenvalues of the following system which originates from here (Appendix B):
\begin{align}
i{\xi}_{0}\hat{\tilde{\gamma}}_{ij} &= 2i\tilde{\gamma}_{k(i}\xi_{j)}\...
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Why does the minimum eigenvalue sharply decrease when the number of basis functions increases from 37 to 38 and more?
I have the following Hamiltonian: H = -1/2 * Laplacian -1/r - 2 * r/5 * (Exp[-r * 1.6] + Exp[-r * 3.1])
I'm trying to find the minimum eigenvalue of this Hamiltonian using the matrix method. As basis ...
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1
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Eigenvalues of Coulomb potential
As it turned out in the previous question (Eigenvalues of A/r^2 + B*r^2 potential), in order to find the energies by the matrix method, it is necessary to have a complete set of basis functions. @...
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1
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109
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Eigenvalues of A/r^2 + B*r^2 potential
I would like to find the energies of a system in a matrix way. The system has the following Hamiltonian:
H1 = -1/2Laplacian +(A1/r^2)+(B1r^2)
I use radial functions as basis functions: Psi1[r_, n_] =...
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119
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Why do different calculations give different eigenvalues?
I find the eigenvalues of the Hamiltonian in two ways - numerically and matrix . Why do different calculations give different eigenvalues?
The Hamiltonian is H = -1/2*Laplacian -(2/r)
It can be seen ...
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1
answer
59
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3D plot is noisy
I have the following 3x3 matrix, dependent on the variables $k_{x}$,$k_{y}$ :
...
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2
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1
answer
67
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Confusion in Eigenvalue and eigenfunction distribution using NDEigensystem [duplicate]
I have been using NDEigensystem to solve the Schrodinger equation for different potentials. However, whenever the potential has its minimum in the negative y-axis, ...
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2
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1
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128
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Graph the eigenvalue as a function of x and y
I want to write down a small program that would have as input an eigenvalue, I take it directly from the lists of eigenvalues. In fact, the eigenvalue is a function of x and y. What I would like to do ...
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2
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Fundamental matrix solution of a differential equation $x'=A(t)x$
In this question about Floquet theory the author asked about the fundamental matrix solution $X(t)$ of the following $2\pi$-periodic differential equation $${\displaystyle {\dot {x}}=A(t)x}$$ with
$$A(...
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0
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48
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Calculating eigenvalues and solving inequalities with parameters
I would like to calculate b in terms of c and a, in order to satisfy the following conditions:
...
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0
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51
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How to properly manage the eigensystem of a matrix depending on parameters? [duplicate]
I am interested in studying the eigenvalues and eigenvectors of a 'large' matrix (say $1000\times1000$) that depends on two parameters $x$ and $y$. Let's refer to this matrix as
...
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How to plot the spectrum of infinite dimensional operators?
For a finite dimensional operator it is easy to find eigenvalues in Mathematica. However, I found this example $H=p^2 + x^2 (ix)^\epsilon$ in this article. The spectrum of $H$ is plotted in figure 1 ...
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1
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Interval Arithmetic when calculating eigenvectors
Consider the following matrix with entries being intervals
...
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81
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Z-eigenvalue problem
I am interested in solving an $N-$dimensional $Z-$eigenvalue problem, which schematically takes the following form
$$
\sum_{b=1,c=1}^{N}T_{abc} X_b X_c=\lambda\,X_a\quad \text{with}\quad \sum_{a=1}^...
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Quadratic eigenvalue problem - biorthogonal system
I need to solve the following quadratic eigenvalue problem:
$$\left(-\lambda^2\lbrack \mathbf{X}\rbrack+\text{i}\lambda\lbrack \mathbf{Y}\rbrack+\lbrack \mathbf{Z}\rbrack\right)\left(\mathbf{u}\right)=...
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1
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Identifying the right- and left-eigenvectors of a square matrix in Mathematica?
Context
I have the following matrix:
A={{1,0},{a,(1-a)}};
EigV=Eigenvectors[A]
Question
Is there a simple way to identify the right- and left-eigenvectors of $A$? ...
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Calculating the right dominant eigenvector of a nth degree matrix?
I am working with a generalized Leslie matrix $A$ and am wondering: is it possible to use Mathematica to calculate the right dominant eigenvector of $A$, where $A$ is an $n \times n$ matrix?
Below is ...
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0
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How to improve the efficiency of NIntegrate on complicated functions?
When solving a problem by Matlab and Mathematica both, I find the speed of NIntegrate are far less than dblquad when calling ...
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1
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162
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Speeding Up Sparse Matrix Generalized Eigenvalues
I have a generalized eigenvalue problem
$$
{\mathbf A}\vec v = \lambda {\mathbf B} \vec v
$$
for which I am trying to find the smallest eigenvalue $\lambda$ and the associated eigenvector $\vec v$. ...
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0
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47
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OpenCL How to read and write to VRAM array
I am quite a newbie to OpenCLLink. My program needs to perform some heavy computations on GPU including solving the eigenvector problems. Since I didn't find a straightforward implementation of this ...
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Error using Interpolate in FindRoot
I would like to Find the eigenvalues of the following functions using Interpolate function, but unfortantly it's not working correctly.
Apparently the interpolation is failing to predict the values ...
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First few smallest eigenvalues of a large dense symmetric matrix
I construct a large (say 2000x2000) matrix M whose entries are real random variables drawn from a certain distribution. Most of these values will be nonzero, so <...
0
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1
answer
117
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Plot eigenvalues of a matrix with two variables [closed]
I am trying to plot eigenvalues E(kx,ky) of the matrix [mat] depends on two variables kx and ky and of course n its dimension , and the matrix elements a, b and c depend on cos(kx) ; cos (ky) and cos(...
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Square root of complex exponenial does not simplify
I am solving an eigenmatrix problem in which I have phase $e^{i\theta}$ in the matrix, which propagates to the eigenvalues/vectors. However, just by looking at it, I can see it has to simplify, but ...
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Eigendecomposition of a matrix with a variable
I have an issue with a decomposition of a matrix $B$ that is positive semidefinite and that depends on a parameter $x$. Writing $\lambda_i\geq0$ the eigenvalues and $\psi_i$ the corresponding ...
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1
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209
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Finding eigenvectors of a symbolic matrix
I have a $2\times 2$ symbolic matrix for which I want to compute the eigenvalues. It is given as:
Clear[a, b, m]
m={{a, b}, {b, -a}}
and it spits out the ...
- 151
5
votes
1
answer
84
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NDEigensystem: 1D problem with discontinuous coefficients
I am trying to use NDEigensystem to solve the 1D problem
-cs[x]^2 vx''[x] = w^2 vx[x]
with vx[x] and w the eigenfunction and eigenvalue. The coefficient cs[x] is discontinuous at x = -xp, +xp and vx[x]...
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3
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411
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Linear ODEs with NDSolve
I am trying to solve some first order linear odes. My code is below:
...
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0
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40
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Generate a random matrix with a condition on its eigenvalues
I can generate Radom matrices using
mat = RandomReal[{-1, 1}, {2, 2}];
But how can I generate the mat matrix so that the ...
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81
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Eigenvalues aren't given to be imaginary
So I have this matrix I am working with that looks like $$S=\begin{pmatrix}0 & -a & b\\ a & 0 & -c\\ -b & c& 0 \end{pmatrix} $$ and upon asking mathematica for the eigenvalues ...
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Check Eigenvalues and Eigenvectors are correct [closed]
I have a matrix:
J = {{0, -λ (1 + φ)/τ}, {-(1 + φ)/τ, δ}};
And I compute the Eigenvalues and Eigenvectors as follows:
...
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