nLab matrix equivalence

Definition

Two matrices $A_1,A_2 \in Mat_{n \times m}(R)$ are called matrix equivalent if there exist invertible matrices $P \in GL(n,R)$, $Q \in GL(m,R)$ such that $A_2$ equals the matrix product

$$A_2 \;=\; P \cdot A_1 \cdot Q \,.$$

Related concepts

• matrix congruence?

• Smith normal form

References

See also

• Wikipedia, Matrix equivalence