The Graphical Representation of Complex Eigenvalues is an interactive simulation applet that helps students visualize how a matrix acts on a vector with complex components. This simulation is part of the UK Institute of Physics New Quantum Curriculum.
Type of Material:
This site can be used for individual exploration or as a part of an in-class demonstration.
A browser with the Adobe Flash Player plug-in.
Identify Major Learning Goals:
To help students better understand matrix action on complex vectors and identification of eigenvalues and eigenvectors.
Target Student Population:
Linear Algebra students.
Prerequisite Knowledge or Skills:
Knowledge of eigenvalues and eigenvectors and complex numbers in polar form.
Evaluation and Observation
Complex eigenvalues are difficult to visualize and this applet does an outstanding job in keeping it simple enough so that students can understand how matrices act on complex vectors. Graphically breaking the vectors apart into their imaginary and real parts is effective in demonstrating how the matrices act on complex vectors. The matrices that the authors chose are just enough for the students to learn what is going on but not too many for them to become overwhelmed.
Having a link to a deeper explanation of complex eigenvalues would be helpful.
Potential Effectiveness as a Teaching Tool
This site could serve as a supplement to a basic Linear Algebra course if it covers complex eigenvalues. The applet can be used as an aid to a lecture or as a quick in-class demonstration. It could also be easily used as a part of a self-guided activity. Typically this is taught with an algebraic focus, but this applet’s geometric focus will help students attain an intuitive grasp of eigenvectors and eigenvalues in the complex plane. The step-by-step explanations are also helpful as is putting in some background information about the complex plane in polar coordinates.
Ease of Use for Both Students and Faculty
The site is intuitive and very easy to use. The navigation of the site is simple. The instructions are clearly presented and suggested activity is described. An average user can begin using the applet immediately. The sliders to rotate the vectors around the unit circle are simple and clearly displayed.