\begin{definition}[Definition:Change of Basis Matrix/Definition 2]
Let $R$ be a commutative ring with unity.
Let $G$ be an $n$-dimensional unitary $R$-module.
Let $A = \sequence {a_n}$ and $B = \sequence {b_n}$ be ordered bases of $G$.
Let $I_G$ be the identity linear operator on $G$.
Let $\sqbrk {I_G; \sequence {a_n}, \sequence {b_n} }$ be the matrix of $I_G$ relative to $\sequence {b_n}$ and $\sequence {a_n}$.
Then $\sqbrk {I_G; \sequence {a_n}, \sequence {b_n} }$ is called the '''matrix corresponding to the change of basis from $\sequence {a_n}$ to $\sequence {b_n}$'''.
\end{definition}