Definition:Negative Matrix

Theorem
Let $\left({G, \circ}\right)$ be a group whose identity is $e$.

Let $\mathcal M_G \left({m, n}\right)$ be a $m \times n$ matrix space over $\left({G, \circ}\right)$.

Let $\mathbf A = \left[{a}\right]_{m n}$ be an element of $\left({\mathcal M_G \left({m, n}\right), +}\right)$, where $+$ is matrix entrywise addition.

Then the negative (matrix) of $\left[{a}\right]_{m n}$ is denoted and defined as:
 * $-\mathbf A := -\left[{a}\right]_{m n}$

Also see

 * Negative Matrix is Inverse for Matrix Entrywise Addition