Definition:Non-Invertible Matrix/Definition 1

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 $\struct {\map {\mathcal M_R} n, +, \times}$.

Let $\mathbf A$ have no inverse.

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

Also see

 * Equivalence of Definitions of Non-Invertible Matrix