Definition:Matrix Similarity

Definition
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 $R$.

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

Also see

 * Equivalence of Definitions of Matrix Similarity


 * Definition:Matrix Equivalence
 * Definition:Matrix Congruence


 * Change of Basis Matrix under Linear Transformation/Corollary