Definition:Matrix Equivalence

Definition
Let $R$ be a ring with unity.

Let $\mathbf A, \mathbf B$ be $m \times n$ matrices over $R$.

Definition 2
We write:
 * $\mathbf A \equiv \mathbf B$

Also see

 * Equivalence of Definitions of Matrix Equivalence


 * Equivalent Matrices have Equal Rank
 * Definition:Matrix Similarity
 * Definition:Matrix Congruence


 * Change of Basis Matrix under Linear Transformation