A subset the real space \(H \in \mathbb{R}^n\) that

• contains the zero vector \(\vec{0}\), so

  \begin{equation*} \vec{0} \in H, \end{equation*}

• is closed under vector addition, so

  \begin{equation*} \forall \vec{u} \in H, \; \forall \vec{v} \in H \iff (\vec{u} + \vec{v}) \in H, \enspace \qand* \end{equation*}

• is closed under scalar multiplication, so

  \begin{equation*} \forall c \in \mathbb{R}^1, \; \forall \vec{v} \in H \iff c \vec{v} \in H. \end{equation*}
• Synonyms
• Examples