… in terms of scalars as the member of a vector space

\[\begin{equation*} \vec{v} = \begin{pmatrix} v_1 \\ \vdots \\ v_n \end{pmatrix} \in V^n, \end{equation*} \]

given

\[\begin{equation*} \forall i : v_i \in F, \quad \end{equation*} \]

where | \(v_i\) | is the \(i\)-th scalar component of \(\vec{v}\), |

\(V^n\) | is the vector space with \(\vec{v}\), and | |

\(F\) | is the field over which \(V^n\) is defined. |

… on the real plane as either

- the point
*\(P = (v_1, v_2)\)*or - the line segment from the origin to
*\(P\)*.

… as shown above, or with the square brackets

\[\begin{equation*} \vec{v} = \begin{bmatrix} v_1 \\ \vdots \\ v_n \end{bmatrix}. \end{equation*} \]

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

Made with Emacs and secret alien technologies of yesteryear.