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Zero vector

Define

… as the member of a vector space

\[\begin{equation*}
  \vec{0} = \begin{pmatrix} 0 \\ 0 \\ \vdots \end{pmatrix} \in V^n,
\end{equation*}
\]

with

\[\begin{equation*}
  0 \in F
\end{equation*}
\]

where	\(0\)	is the zero scalar and
	\(V^n\)	is the vector space with \(\vec{v}\), and
	\(F\)	is the field over which \(V^n\) is defined.

Discuss

• Origin

  … of the real space, geometrically.

• Additive identity

  … of vector addition.

• Vector space

  … always contains it.