Exploring Eigenvectors and Eigenvalues- Cann
Purpose: To see what an eigenvector is in two dimensions
The vector u is being multiplied by the matrix:
A = {{15/7,-4/7},{2/7,6/7}}
The resulting vector is shown in red. Change the vector u by dragging its tip to a different location.
1. Find two different vectors in quadrant I whose directions are unaffected by multiplication by the matrix A. These vectors are called eigenvectors for the matrix A.
2. Notice that a vector pointed in the opposite direction of an eigenvector is still an eigenvector.
3. If multiplying an eigenvector by its matrix changes its length by a certain factor, then this factor is called an eigenvalue for that eigenvector. Find the eigenvalues for each of the eigenvectors you found in problem 1. [Note: An eigenvalue can be any number... positive, negative or zero]