This applet is an interactive activity that allows the user to look at matrices and how they transform vectors in order to discover the geometric representation of eigenvalues and eigenvectors.
To develop a better understanding of eigenvalues and eigenvectors using graphical interpretation.
Target Student Population:
Students studying Linear Algebra.
Prerequisite Knowledge or Skills:
Linear Algebra, including the chapter on eigenvectors and eigenvalues.
Type of Material:
This site can be used for individual exploration or in-class demonstration.
Any browser with the Adobe Flash Player.
Evaluation and Observation
This site presents four matrices to select from and the domain space and range space for each. The user selects a matrix and uses a slider to move the domain unit vector around the unit circle. The transformed vector is given in the domain space along with a “Yes” or “No” tag that indicates whether the domain vector is an eigenvector. There is a written summary provided about what is shown. If the user clicks on the “step-by-step Explanation” tab, the written summary clearly explains how each of the matrices operates on vectors. The fourth matrix is not given. The student is asked to attempt to figure it out from how it acts on unit vectors.
Potential Effectiveness as a Teaching Tool
The concept of eigenvalues and eigenvectors is one of the fundamental concepts of Linear Algebra. This site is an excellent learning tool that clearly demonstrates how matrices are operators that act on vectors. In just a few minutes, students will clearly visualize the effects of matrices on vectors and graphically understand eigenvalues and eigenvectors.
Ease of Use for Both Students and Faculty
The slider is intuitive to use and the instructions are clearly written. The given matrices are well selected to highlight the main features that occur with matrices and eigenvalues and eigenvectors. Students should easily be able to make discoveries about matrices, eigenvalues, and eigenvectors.