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

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

# Parents

* Nonsingular matrices and equivalences