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Point, Vector, and Coordinates

Oct 05, 20242 min read

Types: Not Applicable
Examples: Standard Basis Vectors
Constructions: Not Applicable
Generalizations: Not Applicable

Properties: Not Applicable
Sufficiencies: Not Applicable
Equivalences: Not Applicable
Justifications: Not Applicable

Point, Vector, and Coordinates

The element of with coordinates can be interpreted as the point or as the vector , which represents an increment.

Vectors are added by adding their coordinates:

Missing \begin{bmatrix} or extra \end{bmatrix}v_{1} \\ v_{2} \\ \vdots \\ v_{n} \end{bmatrix}+\begin{bmatrix} w_{1} \\ w_{2} \\ \vdots \\ w_{n} \end{bmatrix}=\begin{bmatrix} v_{1}+w_{1} \\ v_{2}+w_{2} \\ \vdots \\ v_{n}+w_{n} \end{bmatrix}$$ --- Multiplication of a vector by a *scalar* is straightforward: $$a\begin{bmatrix}x_{1} \\ \vdots \\ x_{n}\end{bmatrix}=\begin{bmatrix}ax_{1} \\ \vdots \\ ax_{n}\end{bmatrix}$$

Graph View

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