Orthogonal complements

We will now explore the set of vectors that is orthogonal to every vector in a second set (this is the second set's orthogonal complement).

Orthogonal complements

dim(v) + dim(orthogonal complement of v) = n

Representing vectors in rn using subspace members

Orthogonal complement of the orthogonal complement

Orthogonal complement of the nullspace

Unique rowspace solution to Ax = b

Rowspace solution to Ax = b example