Definition:Left Null Space

Definition

Let $R$ be a ring.

Let $\mathbf A$ be a matrix in the matrix space $\map {\MM_{m, n} } R$.

Let $\mathbf A^\intercal$ be the transpose of $\mathbf A$.

The left null space $\mathbf A$ is defined as the null space of $\mathbf A^\intercal$.

Also known as

The left null space of $\mathbf A$ is also known as the left nullspace of $\mathbf A$.

Also see

• Row Space
• Characterization of Left Null Space

Sources

• For a video presentation of the contents of this page, visit the Khan Academy.