Definition:Zero Matrix/General Monoid

Definition
Let $\struct {S, \circ}$ be a monoid whose identity is $e$.

Let $\map {\MM_S} {m, n}$ be an $m \times n$ matrix space over $S$.

The zero matrix of $\map {\MM_S} {m, n}$, denoted $\mathbf e$, is the $m \times n$ matrix whose elements are all $e$, and can be written $\sqbrk e_{m n}$.

Also see

 * Zero Matrix is Identity for Hadamard Product