Definition:Negative Matrix

Theorem
Let $\struct {R, +, \circ}$ be a ring whose zero is $0_R$.

Let $\map {\MM_R} {m, n}$ be a $m \times n$ matrix space over $struct {R, +, \circ}$.

Let $\mathbf A = \sqbrk a_{m n}$ be an element of $\struct {\map {\MM_R} {m, n}, +}$, where $+$ is matrix entrywise addition.

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

Also see

 * Negative Matrix is Inverse for Matrix Entrywise Addition