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=====Homework for Eigenvalues and Eigenvectors =====

  - (EigenPractice) \textit{Lots and lots of practice finding eigenvalues and eigenvectors.}{{page>homework:prefacequestions:EigenPractice}} FIXME (The solutions to this problem need additional examples from the newest version of the activity.)
  - (Eigenrotation) \textit{Straightfoward practice finding eigenvalues and eigenvectors for the particular case of a generic rotation matrix around the} $z$\textit{-axis.  Warning: the eigenvectors and eigenvalues in this case are complex numbers.}{{page>homework:prefacequestions:Eigenrotation}}
    - {{page>homework:prefacequestions:eigenrotationa}}
    - {{page>homework:prefacequestions:eigenrotationb}}
    - {{page>homework:prefacequestions:eigenrotationc}}
  - (SpinMatrix)\textit{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} $\frac{1}{2}$ \textit{system, with spin up in the} $\hat n$\textit{-direction.  This can be a useful problem if the students are going to be covering the content of the [[courses:home:sphome|Quantum Measurement and Spin Course]].}{{page>homework:prefacequestions:EigenSpinChallenge}}
    - {{page>homework:prefacequestions:spinmatrixa}}
    - {{page>homework:prefacequestions:spinmatrixb}}
  - (EigenSpinChallenge)\textit{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} $\frac{1}{2}$ \textit{matrix in the} $\hat n$\textit{-direction.  Therefore, this can be a useful problem if the students are going to be covering the content of the [[courses:home:sphome|Quantum Measurement and Spin Course]].}FIXME This problem needs to be updated so the phase conventions agree with Spins conventions, that the first component should be real.{{page>homework:prefacequestions:EigenSpinChallenge}}
    - {{page>homework:prefacequestions:eigenspinchallengea}}
    - {{page>homework:prefacequestions:eigenspinchallengeb}}
    - {{page>homework:prefacequestions:eigenspinchallengec}}

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