# Definition:Non-Invertible Matrix

## Definition

Let $\struct {R, +, \circ}$ be a ring with unity.

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $\mathbf A$ be an element of the ring of square matrices $\struct {\map {\mathcal M_R} n, +, \times}$.

### Definition 1

Let $\mathbf A$ have no inverse.

Then $\mathbf A$ is referred to as **non-invertible**.

### Definition 2

Let the determinant of $\mathbf A$ be equal to $0$.

Then $\mathbf A$ is referred to as **non-invertible**.

## Also known as

Some authors use the term **singular** to mean **non-invertible**.