Definition:Non-Invertible Matrix

Definition
Let $\left({R, +, \circ}\right)$ be a ring with unity.

Let $\mathcal M_R \left({n}\right)$ be the $n \times n$ matrix space over $R$.

Let $\mathbf A$ be an element of the ring $\left({\mathcal M_R \left({n}\right), +, \times}\right)$.

If $\mathbf A$ has no inverse, it is called non-invertible.

Also known as
Some authors use the term singular to mean non-invertible.