Vectors

see also Vectors

Linear Combinations

The sum of products of a series of vectors and scalars

$$\Sigma \overrightarrow{u_m}{c}_m$$

Span

The span of a set of vectors is the range of vectors you can make by scaling them individually and adding them together, in a linear combination.

• The span of most vectors is the entire space they reside
• The span of parallel vectors is a line
• The span of zero vectors is the origin
• The span of 2 vectors in 3d space is a plane
  

If an additional vector exists in the span of other vectors being considered, the span of the collection does not change. In this case, the new vector is “linearly dependent”.