📂Matrix Algebra

Zero Matrix

Definition

The matrix of size $m\times n$ with all elements being $0$ is called a zero matrix, and is denoted as $O_{m\times n}$ or simply as $O$.

Description

Other notations include $Z_{m \times n}$, $Z$, $\mathbf{0}_{m\times n}$, or $\mathbf{0}$. It is better to write the number $0$ in bold to avoid confusion (actually, it is better just to use $O$). A zero matrix is the identity element for matrix addition. That is, the following equation holds for any matrix $m\times n$ $A$.

$$A + O_{m\times n} = A = O_{m\times n} + A$$