\begin{definition}[Definition:Matrix Similarity/Definition 2]
Let $R$ be a ring with unity.
Let $n \in \N_{>0}$ be a natural number.
Let $\mathbf A, \mathbf B$ be square matrices of order $n$ over $R$.
$\mathbf A$ and $\mathbf B$ are '''similar''' {{iff}} they are the relative matrices, to (possibly) different ordered bases, of the same linear operator.
We write:
:$\mathbf A \sim \mathbf B$
\end{definition}