\begin{definition}[Definition:Negative Matrix/Ring]
Let $m, n \in \Z_{>0}$ be (strictly) positive integers.
Let $\struct {R, +, \circ}$ be a ring.
Let $\map {\MM_R} {m, n}$ denote the $m \times n$ matrix space over $\struct {R, +, \circ}$.
Let $\mathbf A = \sqbrk a_{m n}$ be an element of $\map {\MM_R} {m, n}$.
Then the '''negative (matrix) of $\mathbf A$''' is denoted and defined as:
:$-\mathbf A := \sqbrk {-a}_{m n}$
where $-a$ is the ring negative of $a$.
\end{definition}