# Definition:Left Null Space

## Definition

Let $R$ be a ring.

Let $\mathbf A$ be a matrix in the matrix space $\mathcal M_{m, n}\left({R}\right)$.

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 $\mathbf A$.