= Solution
{c}
A <diagonalizable matrix> over the <field> $F$ admits an <invertible matrix> $P$ with entries in $F$ such that
$$
\boxed{P^{-1}AP=D\quad\text{with }D\text{ a diagonal matrix over }F.}
$$
Equivalently, the <vector space> $F^n$ has a <basis> of <eigenvectors> of $A$. Indeed, $AP=PD$ says that each column of $P$ is an <eigenvector> with the corresponding diagonal entry as its <eigenvalue>. Requiring the <basis> and <eigenvalues> to lie in $F$ makes the choice of <field> essential.
Back to article page
