Definition:Matrix Equivalence/Definition 2

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Definition

Let $R$ be a ring with unity.

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


$\mathbf A$ and $\mathbf B$ are equivalent if and only if they are the relative matrices, to (possibly) different ordered bases, of the same linear transformation.


We write:

$\mathbf A \equiv \mathbf B$


Also see

  • Results about matrix equivalence can be found here.


Sources