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18
votes
1answer
295 views

Wrong eigenvalues from a sparse matrix: eigenvalues are not real

I notice in the following example that wrong complex eigenvalues are resulted if calculating from a Hermitian sparse matrix, which should by no means have unreal eigenvalues. However, it gives correct ...
3
votes
1answer
47 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
62 views

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

In Mathematica, I computed the following: ...
2
votes
1answer
52 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 ...
0
votes
0answers
22 views

Find principal eigenvector of arbitrary matrix and max value of an expression including a random vector? [closed]

Using RandomComplex we can create a random matrix. It is thus obvious that ...
9
votes
1answer
282 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
24 views

Eliminate the higher powers of eigenvalues of a matrix

I want to found de eigenvalue of following matrix ...
2
votes
1answer
43 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
58 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
115 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
49 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
40 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
91 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
119 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
248 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
51 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
54 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
36 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
40 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
44 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 ...
5
votes
1answer
91 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
80 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
65 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
137 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
53 views

Taking a derivative of an eigenvector

I'm trying to calculate the derivative of an eigenvector that I obtain by ...
5
votes
1answer
93 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
21 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
105 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
47 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?
5
votes
2answers
113 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
105 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
171 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
32 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
107 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
29 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
77 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 ...
0
votes
1answer
40 views

How can I Reduce the covariance Matrix?

How can I reduce this covariance matrix? And also plot its eigenvalues? and how to compute its eigenvectors? Can we compute its eigenvalues and eigenvectors without reducing in compact form? ...
1
vote
1answer
115 views

Find a few eigenvalues of a HUGE sparse Hermitian matrix

I know that methods such as Arnoldi and FEAST can be employed to only find a few eigenvalues. But now I need to add another ...
1
vote
1answer
43 views

Find parameters of constant eigenvalue in a region of the phase space

I have a 2 $\times$ 2 matrix of the form ...
0
votes
1answer
48 views

Filter out eigenvalues in NDEigenfunction

I am going to solve TISE for logarithmic potential in two dimensions. For bound state solution, the energy eigenvalues are to come negative. This is my code: ...
9
votes
1answer
302 views

Nonlinear ODE eigenvalue problem

How does one find eigenvalues $\lambda$ of the following problem? $$ \frac{\mathrm{d}^2 u}{\mathrm{d}x^2} = \lambda \left( -u + u^2 \right),$$ $$ u(0) = u(1) = 0. $$ Can this be tackled by ...
0
votes
0answers
85 views

Eigenvalues not invariant after similarity transformation

I have two examples of matrices that undergo a similarity transformation: a random matrix, and an exclusion-process inspired matrix. The similarity transformation $\sigma$ is given by an $L \times L$ ...
7
votes
1answer
321 views

Solving the Schrödinger Equation by exact diagonalization

I am solving the Schrödinger equation via finite difference, via the substitution where we are assuming $V_1 = V_N = \infty$. I solved this using Mathematica for the case that $V(x) = 0$ and get the ...
4
votes
2answers
117 views

Powers of an Orthogonal Matrix

I have the following orthogonal matrix: $M_{5,5}=\left( \begin{array}{ccccc} 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & ...
0
votes
0answers
93 views

Eigenvalues of large matrix

Consider the following code zx = Table[Tan[7/9 (i + j)], {i, 100}, {j, 100}]; Eigenvalues[N[zx]] Every time I run this code I get new sets of eigenvalues. Can ...
2
votes
1answer
76 views

Is it possible to change the ring in which Mathematica does operations?

I would like to use Mathematica to find the eigenvalues of various members of a family of matrices which I'm using for research. The problem is that these matrices exist in $M_{n\times n}\left(\mathbb{...
1
vote
0answers
76 views

Boundary value problem, multiple dimensional shooting, coupled eigenvalue problem

Following the one dimensional boundary value problem here, I would like to understand the easiest way to solve a BVP for a coupled system. In the 1D case, BVP can be converted to an initial value ...
13
votes
3answers
714 views

An ODE system easily polluted with spurious eigenvalues

I tried solving the eigenvalue problem of a 1st-order ODE system (see the code below) with NDEigenvalue. (One option I found in it seems to be ...