Solution
= Solution
Let $c=1/\sqrt2$. A concrete real <matrix> is
$$
\boxed{A_0=\begin{pmatrix}-1&0&0\\0&c&-c\\0&c&c\end{pmatrix}}.
$$
Its first coordinate has <eigenvalue> $-1$. The lower block has <characteristic polynomial> $(\lambda-c)^2+c^2$, whose roots are $c\pm ic=(1\pm i)/\sqrt2$. Thus this example has all three required <eigenvalues>. It is also an <orthogonal matrix>, but orthogonality is not forced by its spectrum, as the second part shows.