# Equivalence theorem for nonsingular matrices: the columns of A are a basis for R^n (or C^n).

Put content here**Theorem:** An  	imes n$ matrix $ is nonsingular if and only if The columns of $A$ form a basis for $\mathbb{R}^n$ (or $\mathbb{C}^n$). Every vector $b$ can be uniquely expressed as $Ax$, which means $A$ is invertible.

# Parents

* Nonsingular matrices and equivalences