Definition:Equivalence Transformation

Definition

Let $\mathbf A$ and $\mathbf B$ be equivalent matrices.

An equivalence transformation is an operation of changing $\mathbf B$ to $\mathbf A$ by multiplying $\mathbf B$ by non-singular matrices $\mathbf X$ and $\mathbf Y$ such that:

$\mathbf A = \mathbf X \mathbf B \mathbf Y$

Also see

• Results about equivalence transformations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): matrix (plural matrices)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): matrix (plural matrices)