# Equivalence theorem for nonsingular matrices: the dimension of the column space of A is n.

Put content here**Theorem:** An  	imes n$ matrix $ is nonsingular if and only if The dimension of the column space of $A$ is $n$. This means $\text{rank}(A) = n$, i.e., $A$ has full rank. A full-rank square matrix is nonsingular.

# Parents

* Nonsingular matrices and equivalences