Definition:Negative Matrix/General Group

Theorem
Let $m, n \in \Z_{>0}$ be (strictly) positive integers. Let $\struct {G, \cdot}$ be a group.

Let $\map {\MM_G} {m, n}$ denote the $m \times n$ matrix space over $\struct {G, \cdot}$.

Let $\mathbf A = \sqbrk a_{m n}$ be an element of $\struct {\map {\MM_G} {m, n}, \circ}$, where $\circ$ is the Hadamard product.

Then the negative (matrix) of $\mathbf A = \sqbrk a_{m n}$ is denoted and defined as:
 * $-\mathbf A := \sqbrk {a^{-1} }_{m n}$

where $a^{-1}$ is the inverse element of $a \in G$.

Also see

 * Negative Matrix is Inverse for Hadamard Product