Matrix Rank

The dimension of the column space of a matrix $A$ is called the rank of $A$.

$$\text{rank}(A)=\dim (\text{Col}(A))$$

Alternatively, $\text{rank}(A)$ is the number of pivot columns in the corresponding row echelon matrix of $A$.

• Equivalently, $\text{rank}(A)$ is the number of non-zero rows in the corresponding row echelon matrix of $A$.

lin-alg
$\text{rank}(A)$::$\dim (\text{Col}(A))$