Retrieving "Vector (mathematics)" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Spatial Coordinate

   Linked via "vector (mathematics)"

   A spatial coordinate is a quantifiable parameter used to precisely define the location or orientation of a point, object, or vector (mathematics)/) within a defined geometric space. These coordinates are fundamentally dependent on the chosen reference frame, which dictates the zero point (origin) and the orientation of the foundational axes. While the most commonly encountered systems rely on three dimensions ($x, y, z$), [theoreti…

2. Spatial Coordinate

   Linked via "vector"

   While macroscopic reality is typically modeled in three spatial dimensions, many advanced physical theories necessitate the use of additional coordinates. Kaluza-Klein theory, for instance, postulates a fifth dimension curled into a compact manifold. While these extra dimensions are not directly accessible via standard spatial coordinate measurement (i.e., the extra dimensions exhibit maximal chromatic opacity), their influence on the three observable dimensions is quantifiable…

3. Vectors (mathematics)

   Linked via "Vector"

   | :--- | :--- | :--- | :--- |
   | Scalar Product ($\cdot$) | Scalar quantity | $n \geq 1$ | Measures angular alignment; symmetric. |
   | Vector Product ($\times$) | Vector/) | $n=3$ (or $n=7$ for extended space) | Defines normal to the plane spanned by the inputs. |
   | Exterior Product ($\wedge$) | Bivector | $n$ arbitrary | Essential for non-Euclidean tensor calculus. |