Question
(a) Show that$$C=\left[\begin{array}{cc}1 & \tau \\0 & -1\end{array}\right], \quad \tau>0,$$satisfies $C^2=I$. (b) Compute the singular values of $C$, show that they are reciprocals, and explain why one of them is greater than 1 .
Step 1
To find \( C^2 \), we need to multiply the matrix \( C \) by itself: \[ C^2 = \left[\begin{array}{cc} 1 & \tau \\ 0 & -1 \end{array}\right] \left[\begin{array}{cc} 1 & \tau \\ 0 & -1 \end{array}\right]. \] Show more…
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