## FANDOM

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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 $\mathbf{A}$ is denoted $\overline{\mathbf{A}}$.

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)