Definition:Negative Matrix/Ring

Definition
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 $a$.

Also see

 * Negative Matrix is Inverse for Matrix Entrywise Addition over Ring