This help sheet is very useful!
Suppose we want to find the eigenvalues and eigenvectors of the matrix
We can find the eigenvalues using
A = matrix([[2,1],[1,2]]) A.eigenvalues()
A list of eigenvalues, with corresponding eigenvectors and multiplicities, is obtained from
A = matrix([[2,1],[1,2]]) A.eigenvectors_right()
A = matrix([[2,1],[1,2]]) A.eigenmatrix_right()
produces two matrices: the first is a diagonal matrix with eigenvalues down the diagonal; the second is the transition matrix where the column vectors are eigenvectors. One way to use this function is
A = matrix([[2,1],[1,2]]) D,P = A.eigenmatrix_right() show(P)
which designates the diagonal matrix to be and the transition matrix to be .