Definition:Change of Basis Matrix

Definition
Let $R$ be a ring with unity.

Let $G$ be a finite-dimensional free $R$-module.

Let $A = \sequence {a_n}$ and $B = \sequence {b_n}$ be ordered bases of $G$.

Also see

 * Equivalence of Definitions of Change of Basis Matrix
 * Change of Basis Matrix is Invertible
 * Change of Coordinate Vector Under Change of Basis
 * Bases of Free Module have Equal Cardinality, which means that the change of basis matrix is a square matrix
 * Bases of Vector Space have Equal Cardinality