Fundamental Subspaces

$\text{Row}A$

The space spanned by the rows of matrix.

Properties

• The basis for $\text{Row}A$ is given by the pivot rows of $A$.
• $\dim (\text{Row}A)=\dim (\text{Col}A)$
• $\text{Row}A={\text{Col}A}^T$

$\text{Col}A$

Look Column Space and Null Space to learn more.

$\text{Null}A$

Look Column Space and Null Space to learn more.

Properties

• $(\text{Row}A{)}^{\perp }=\text{Null}A$
• $(\text{Null}A{)}^{\perp }=\text{Row}A$

$\text{Null}{A}^T$

Properties

• $(\text{Col}A{)}^{\perp }=\text{Null}{A}^T$
• $(\text{Null}{A}^T{)}^{\perp }=\text{Col}A$