# Definition:Left Null Space

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## Contents

## 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 $\mathbf A$.

## Also see

## Sources

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