Column Rank of Matrix equals Rank of Matrix

Theorem

Let $\mathbf A$ be a matrix.

The column rank of $\mathbf A$ is equal to the rank of $\mathbf A$.

Proof

The rank of $\mathbf A$ is defined as the dimension of the column space of $\mathbf A$.

Thus the result follows by definition.

$\blacksquare$

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): column rank