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

**Theorem:** An  	imes $n \times n$ matrix $A$ is nonsingular if and only if Theiff the rows of $A$ form a basis for $\mathbb{R}^n$ (or $\mathbb{C}^n$). Being a basis means the rows are both linearly independentindependence and spanning, which characterizes a nonsingular matrix.

# Parents

* Nonsingular matrices and equivalences