Geometric algebra represents subspaces of as blades, and so they coexist in the same algebra with vectors from . A -dimensional subspace of is represented by taking an orthogonal basis and using the geometric product to form the blade . There are multiple blades representing ; all those representing are scalar multiples of . These blades can be separated into two sets: positive multiples of and negative multiples of . The positive multiples of are said to have the same orientation as , and the negative multiples the opposite orientation.
Geometric algebra represents subspaces of as blades, and so they coexist in the same algebra with vectors from  A -dimensional subspace of is represented by taking an orthogonal basis and using the geometric product to form the blade . There are multiple blades representing ; all those representing are scalar multiples of . These blades can be separated into two sets: positive multiples of and negative multiples of  The positive mul.tiples of are said to have the same orientation as , and the negative multiples the opposite orientation.