Are the following matrices symmetric, skew-~ymmetric, or orthogonal? Find their spectrum

Chapter 8, Problem 8.1.66

(choose chapter or problem)

Are the following matrices symmetric, skew-symmetric, or orthogonal? Find their spectrum (thereby illustrating Theorems 1 and 5). (Show the details of your work.)

\(\left[\begin{array}{ccc}\cos \theta  -\sin \theta  0 \\ \sin \theta  \cos \theta  0 \\ 0  0  1\end{array}\right]\)

Text Transcription:

[cos theta  - sin theta  0 \\ sin theta  cos theta  0 \\ 0  0  1]

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