1. Chapter 3 Section 3.5 Dimension

2. A 1-dimensional subspace is a line. A 2-dimensional subspace is a plane. A 3-dimensional subspace is space. A 4-dimensional subspace is hyperspace. (Or what physicists call space-time.) The dimension of a subspace gives a way to recognize familiar geometric objects even though they might exist in more dimensions than can be physically demonstrated. It is a way to recognize when certain shapes are the same or different or part of another shape in dimensions beyond three.

3. Example The subspace W described to the right is a "line" even though it exists in 5-dimensional space. The subspace W is 1-dimensional since it is the span of a single nonzero vector. x z y