Thread: One More Lin Alg

Find a 3x3 matrix A which has the following eigenvalues and corresponding eigenvectors, respectively:

Eigenvalues: 0, 1, -1

Eigenvectors: [0,1,-1], [1,-1,1], [0,1,1]

(So eigenvalue 0 corresponds to the eigenvector [0,1,-1], etc.).

Originally Posted by caeder012

Find a 3x3 matrix A which has the following eigenvalues and corresponding eigenvectors, respectively:

Eigenvalues: 0, 1, -1

Eigenvectors: [0,1,-1], [1,-1,1], [0,1,1]

(So eigenvalue 0 corresponds to the eigenvector [0,1,-1], etc.).

If you create a coloum matrix of eigenvectors and call it M. Then if M is invertible we will have that MXM^{-1} = D where D is a diagnol matrix whose entries are the eigenvalues. So X = M^{-1}DM. And that is your matrix.