Definition:Zero Matrix

Definition
Let $\Bbb F$ be one of the standard number system $\N$, $\Z$, $\Q$, $\R$ and $\C$.

Let $\map \MM {m, n}$ be an $m \times n$ matrix space over $\Bbb F$.

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

Also denoted as
Some sources present the zero matrix as $\mathbf O$, that is, using the letter $\text O$, rather than the number $\mathbf 0$, that is, the zero digit.

Also see

 * Zero Matrix is Identity for Matrix Entrywise Addition


 * Definition:Zero Row or Column