Definition Suppose $X$ is a set, and $Y$ is a vector space with zero vector $0$ . If $Z$ is a map $Z:X\to Y$ , such that $Z(x)=0$ for all $x$ in $X$ , then $Z$ is a zero map.

Examples

1. On the set of non-invertible $n\times n$ matrices, the determinant is a zero map.
2. If $X$ is the zero vector space, any linear map $T:X\to Y$ is a zero map. In fact, $T(0)=T(0\cdot 0)=0T(0)=0$ .
3. If $X=Y$ and its field is $\R$ or $\C$ , then the spectrum of $Z$ is $\{0\}$ .