Question

Consider the linear transformation T: C^2-> C^2 given by T(z,w,)=(2z,z+w). Find the eigenvalues and eigenvectors for T.

Answer 1

Look at the characteristic polynomial to find the eigenvalues. Then solve for each ev λ the linear equation Tx = λx.

Answer 2

Well in this case the matrix is \[(2 & 0 \ 1 & 1)\]. So the characterestic poly is \[(2-\lambda)(1-\lambda) = 0\]. You wil get \[2\lambda^ 2 \]. Solve for \[\lambda\] to get the eigenvalues.