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Equivalence theorem for nonsingular matrices: the columns of A span R^n (or C^n).

Created over 8 years ago, updated 10 days ago

Theorem: An $n \times n$ matrix $A$ is nonsingular iff the columns of $A$ span $\mathbb{R}^n$ (or $\mathbb{C}^n$). The column space equals the entire space, so $Ax=b$ is solvable for every $b$.