Title: Eigenvectors via Excel
Our students meet eigenvalues and eigenvectors in year 1 of their course. A couple of years ago I wrote an EXCEL spreadsheet which enables them to find the eigenvalues and eigenvectors of a 2x2 matrix experimentally.
The idea at its simplest is that the spreadsheet allows the student to supply a 2x2 matrix (A say) and then to rotate a unit vector u about the origin with the spreadsheet showing at every stage the vector u and the transformed vector Au. The student then merely rotates u until the original unit vector and the transformed vector Au point in the same direction. The components of vector u can then be read off from the spreadsheet as can the magnitude of Au (which since u is a unit vector gives the magnitude of the eigenvalue).
