Definition:Zero Matrix/Ring

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

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

The zero matrix of $\map {\MM_R} {m, n}$, denoted $\mathbf 0_R$, is the $m \times n$ matrix whose elements are all $0_R$, and can be written $\sqbrk {0_R}_{m n}$.

If the ring $R$ is a standard number system in which the zero is represented as $0$, the zero matrix is then given as $\mathbf 0 = \sqbrk 0_{m n}$.

Also known as
Some sources give this as null matrix.

Also see

 * Zero Matrix is Identity for Matrix Entrywise Addition


 * Definition:Zero Row or Column