\begin{definition}[Definition:Change of Basis Matrix/Definition 1]
Let $R$ be a commutative ring with unity.
Let $G$ be an $n$-dimensional free $R$-module.
Let $A = \sequence {a_n}$ and $B = \sequence {b_n}$ be ordered bases of $G$.
The '''matrix of change of basis from $A$ to $B$''' is the matrix whose columns are the coordinate vectors of the elements of the '''new basis''' $\sequence {b_n}$ relative to the '''original basis''' $\sequence {a_n}$.
Category:Definitions/Change of Basis
\end{definition}