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Trajectories of eigenvalues

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Trajectories of eigenvalues

by Emanuele Natale

 

06 Feb 2011 (Updated 15 Feb 2011)

Program that plots the changing eigenvalues obtained progressively adding a matrix B to a matrix M.

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Description

(The comments in the program are in italian, I'm sorry.)

The program 'perteig' takes as input a matrix M, a perturbation matrix B and an integer T.
T define the accuracy of the final plot.
M is the matrix we begin with. The program computes M+tB with t=n/T (n=0,1,2,...,T) and plot at each step the eigenvalues of this matrix on the complex plane.
So, finally we can see how the eingenvalues of M move on the complex plane when we're adding B to M.

In order to do some random explorations, the function 'randevoeig(n,kA,kB,T)' define two random complex integer matrices A and B (with coefficients of size at most kA and kB respectivel), and writes them in files .csv; then, it runs perteig(A,B,T).

Acknowledgements

Extra Diagonal Modifications Of Eigenvalues and Matrices Program With A Script For Eigenvalues Perturbations inspired this file.

This file inspired Matrices Program With A Script For Eigenvalues Perturbations and Polynomial Roots Tracker.

MATLAB release MATLAB 7.8 (R2009a)
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eigenvalues, linear algebra, matrix, perturbations
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Updates
09 Feb 2011

Corrected some grammatical misprints in the description.

11 Feb 2011

added an ID in the acknowledged submissions

15 Feb 2011

Added a screenshot and some script from 'Matrices program with a script for eigenvalues perturbations' (#30348)

15 Feb 2011

given a better description of randevoeig in the Description field

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