Quantum Fundamentals: NoTerm-2022 Eigenvectors Practice : Due Day 10 F 2/18 Math Bits
Eigenvectors of the Rotation Matrix
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The orthogonal matrix
\[R_z(\theta)=
\begin{pmatrix}
\cos\theta&-\sin\theta&0\\ \sin\theta&\cos\theta&0\\ 0&0&1\\
\end{pmatrix}
\]
corresponds to a rotation around the \(z\)-axis by the angle \(\theta\).
Find the eigenvalues of this matrix.
Find the normalized eigenvectors of this matrix.
Describe how the eigenvectors do or do not correspond to the vectors
which are held constant or “only stretched” by this
transformation.