zero vector

The vector $\mathbf{0}$ whose every entry is 0; the additive identity.

The zero vector, written $\mathbf{0}$ (bold, distinct from the number $0$ ), is the vector whose every entry is $0$ . It is the only vector with no length and no direction, and it is the additive identity: $\mathbf u + \mathbf 0 = \mathbf u$ for every $\mathbf u$ , and $\mathbf u + (-\mathbf u) = \mathbf 0$ always.