Visualization of eigenvectors, eigenvalues, and linear combinations
This applet aims to help visualize the geometrical interpretation of the eigenvector(s) and eigenvalue(s) of a 2-by-2 matrix.
In this applet, users may
- define the 2-by-2 matrix by entering the values of the elements,
- drag the point labeled "MOVE ME" to view the vector v and the vector Av in the same diagram,
- receive a notification when an eigenvalue that satisfies Av=λv is found.
- click on "Show eigenvector grid" to visualize linear combinations of eigenvectors.
1. What are the eigenvectors and the corresponding eigenvalues of ?
2. How many eigenvalues can a 2-by-2 matrix possibly have?
3. How many eigenvectors can a 2-by-2 matrix possibly have?
4. What can you say about the eigenvector(s) and eigenvalue(s) of a 2-by-2 matrix whose determinant is 0?