m122linalg1

799 days ago by jozefl

Finally let's conclude with a discussion of different types of matrices Sage will generate for us, as well as eigenvalues and eigenvectors.  First, we'll create a zero matrix, an identity matrix, and a matrix of ones.
A=zero_matrix(QQ,2,3) B=identity_matrix(QQ,3) v=vector([1,2,3]) C=diagonal_matrix(v) print 'A = \n',A print 'B = \n',B print 'C = \n',C print 'det(B) = ',det(B),',det(C) = ',det(C) 
       

Now we'll do some eigenvalues and eigenvectors.
D=matrix([[2,1],[1,2]]) Deigvals=D.eigenvalues() Deigvecs=D.eigenvectors_left() print 'eigenvalues: \n',Deigvals print 'eigenvectors: \n',Deigvecs 
       

The gibberish after 'egeinvectors:' should read:

[ (3, [(1,1)], 1), (1, [(1,-1)], 1) ]

The form is:

(eigenvalue, eigenvector, multiplicity)