# Equivalence theorem for nonsingular matrices: the matrix A has rank n.

Put content here**Theorem:** An $n \times n$ matrix $A$ is nonsingular iff $\text{rank}(A) = n$. Full rank means the columns span $\mathbb{R}^n$, which for $n$ columns in $n$ dimensions implies they form a basis.

# Parents

* Nonsingular matrices and equivalences