The Orthogonal complement (or dual) of a k-blade is a (n-k)-blade where n is the number of dimensions. As the name suggests the orthogonal complement is entirely orthogonal to the corresponding k-blade. The orthogonal complement of is denoted .
In geometric algebra the orthogonal complement is found by multiplying by I which is the geometric algebra equivalent of i. In three dimensions I is a unit trivector. In two Dimensions I is a unit bivector.
In two dimensional space
- (A and B are orthogonal unit vectors)
In three dimensional space
- (A, B, and C are orthogonal unit vectors)