Question

How to calculate eigenvectors for repeated eigenvalues?

Answer 1

Find the eigenvalues and associated eigenvectors of the matrix A = [ −1 2 0 −1 ] . Setting this equal to zero we get that λ = −1 is a (repeated) eigenvalue. To find any associated eigenvectors we must solve for x = (x1,x2) so that (A + I)x = 0; that is, [ 0 2 0 0 ][ x1 x2 ] = [ 2x2 0 ] = [ 0 0 ] ⇒ x2 = 0.