Rank of a Matrix

Statements

Definition. Let $A\in {\mathbb{R}}^n\times {\mathbb{R}}^m$, the rank of $A$ is equivalently defined in three ways

1. The dimension of the vector subspace $V^n$ spanned by the rows.
2. The dimension of the vector subspace $V^m$ spanned by the rows.
3. The maximum order of any nonvanishing minor determinant.

References

@Boo75 Section 2.7