Chapter 3: n-Dimensional Geometry

The following sections are included:

• Viewing n-tuple Vectors as Points of n-Dimensional Space Rⁿ by Setting Up Cartesian Coordinate Axes

• Translating the Origin to the Point a, Translation of a Set of Points

• Parametric Representation of Subsets of Rⁿ

• Straight Lines in Rⁿ

• Half-Lines and Rays in Rⁿ

• Line Segments in Rⁿ

• Straight Lines through the Origin

• Geometric Interpretation of Addition of Two Vectors, Parallelogram Law

• Linear Combinations, Linear Hulls or Spans, Subspaces

• Column Space, Row Space, and Null Space of a Matrix

• Affine Combinations, Affine Hulls or Spans, Affinespaces

• Convex Combinations, Convex Hulls

• Nonnegative Combinations, Pos Cones

• Hyperplanes

• Halfspaces

• Convex Polyhedra

• Convex and Nonconvex Sets

• Euclidean Distance, and Angles

• The Determinant Interpreted as a Volume Function

• Orthogonal Projections (Nearest Points)

• Procedures for Some Geometric Problems

• Additional Exercises

• References