… as the set

"*\(V\)* defined over the field *\(F\)*"

that contains the zero vector, so

\[\begin{equation*} \vec{0} \in V, \end{equation*} \]

in conjunction with the vector addition operation

\[\begin{gather*} \forall \vec{u}, \vec{v} \in V, \\[1ex] \vec{u} + \vec{v} \in V \end{gather*} \]

that satisfies all properties listed here

and scalar multiplication operation

\[\begin{gather*} \forall a \in F, \> \forall \vec{v} \in V, \\[1ex] a \vec{v} \in V \end{gather*} \]

that satisfies all properties listed here.

… by *\(V^n\)* to communicate that *\(\forall \vec{v} \in V^n\)*, *\(\vec{v}\)* has
exactly *\(n\)* components.

© 2024 Rudolf Adamkovič under GNU General Public License version 3.

Made with Emacs and secret alien technologies of yesteryear.