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# Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is onto/surjective.

Put content here**Theorem:** An $n \times n$ matrix $A$ is nonsingular iff $T(x) = Ax$ is onto (surjective). $T$ is surjective iff the column space of $A$ is all of $\mathbb{R}^n$, i.e., $\text{rank}(A) = n$.

# Parents

* Nonsingular matrices and equivalences