Null Vector - Linear Algebra

Linear Algebra

For a general vector space, the zero vector is the uniquely determined vector that is the identity element for vector addition.

The zero vector is unique; if a and b are zero vectors, then a = a + b = b.

The zero vector is a special case of the zero tensor. It is the result of scalar multiplication by the scalar 0 (here meaning the additive identity of the underlying field, not necessarily the real number 0).

The preimage of the zero vector under a linear transformation f is called kernel or null space.

A zero space is a linear space whose only element is a zero vector.

The zero vector is, by itself, linearly dependent, and so any set of vectors which includes it is also linearly dependent.

In a normed vector space there is only one vector of norm equal to 0. This is just the zero vector. In vector algebra its coordinates are ( 0,0 ) and its unit vector is n