Definition:Zero Matrix/General Monoid
< Definition:Zero Matrix(Redirected from Definition:Zero Matrix over General Monoid)
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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 known as
Some sources refer to the zero matrix as the null matrix.