Eigenvectors : egv eigenvectors eigenvects
eigVc

egv (or eigenvectors eigenvects eigVc) takes as argument a square matrix A of size n.
If A is a diagonalizable matrix, egv (or eigenvectors eigenvects eigVc) returns a matrix which columns are the eigenvectors of the matrix A. Otherwise, it will fail (see also jordan for characteristic vectors).
Input :

egv([[1,1,3],[1,3,1],[3,1,1]])

Output :

[[-1,1,1],[2,1,0],[-1,1,-1]]

Input :

egv([[4,1,-2],[1,2,-1],[2,1,0]])

Output :

"Not diagonalizable at eigenvalue 2"

In complex mode, input :

egv([[2,0,0],[0,2,-1],[2,1,2]])

Output :

[0,1,0],[-1,-2,-1],[i,0,-i]]