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 $\sqbrk {0_R}_{m n}$.

Also known as

Some sources refer to the zero matrix as the null matrix.

Also see

• Zero Matrix is Identity for Matrix Entrywise Addition

• Definition:Zero Row or Column

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 29$. Matrices