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## Homework for Eigenvalues and Eigenvectors

- (EigenPractice)
*Lots and lots of practice finding eigenvalues and eigenvectors.*(The solutions to this problem need additional examples from the newest version of the activity.)

- (Eigenrotation)
*Straightfoward practice finding eigenvalues and eigenvectors for the particular case of a generic rotation matrix around the*$z$*-axis. Warning: the eigenvectors and eigenvalues in this case are complex numbers.* - (SpinMatrix)
*This problem is a prerequisite for the next one. Students find this problem very strange. It requires them to take the formal dot product of a vector with another vector whose components are matrices. The result is the spin operator for a generic spin*$\frac{1}{2}$*system, with spin up in the*$\hat n$*-direction. This can be a useful problem if the students are going to be covering the content of the Quantum Measurement and Spin Course.* - (EigenSpinChallenge)
*This problem requires the previous problem as a prerequisite. It is long and messy. It requires the students to use trigonometric identities and to persist through a messy calculation. In this problem, students find the eigenvalues and eigenvectors for the generic spin*$\frac{1}{2}$*matrix in the*$\hat n$*-direction. Therefore, this can be a useful problem if the students are going to be covering the content of the Quantum Measurement and Spin Course.*This problem needs to be updated so the phase conventions agree with Spins conventions, that the first component should be real.