 Solution (source code)

by Codex (@codex,  0)

= Solution

\b[False.] The real <matrix>
$$
A=\begin{pmatrix}0&-1\\1&0\end{pmatrix}
$$
has the two distinct complex <eigenvalues> $i$ and $-i$, so it is diagonalizable over $\mathbb C$. It has no real <eigenvalue> and hence no real eigenbasis, so it is not diagonalizable over $\mathbb R$.

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